Matthias Georg Hieber

教授(任期付)

  • 1777 Citations
  • 17 h-Index
1989 …2019
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Research Output 1989 2019

  • 1777 Citations
  • 17 h-Index
  • 69 Article
  • 5 Chapter
  • 3 Conference contribution
  • 2 Editorial
2019
Nematic liquid crystals
Topology
Nematic Liquid Crystal
Equilibrium Point
Global Solution

Optimal decay rates for solutions to the incompressible Oldroyd-B model in R 3

Hieber, M. G., Wen, H. & Zi, R., 2019 Jan 29, In : Nonlinearity. 32, 3, p. 833-852 20 p.

Research output: Contribution to journalArticle

Decay Estimates
Decay Rate
decay rates
Weak Solution
Large Data
2018
1 Citation (Scopus)

Modeling and analysis of the ericksen-leslie equations for nematic liquid crystal flows

Hieber, M. G. & Prüss, J. W., 2018 Apr 19, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer International Publishing, p. 1075-1134 60 p.

Research output: Chapter in Book/Report/Conference proceedingChapter

Nematic liquid crystals
Nematic Liquid Crystal
liquid crystals
compressible fluids
incompressible fluids
1 Citation (Scopus)

On the bidomain problem with FitzHugh–Nagumo transport

Hieber, M. G. & Prüss, J., 2018 Jun 14, (Accepted/In press) In : Archiv der Mathematik. p. 1-15 15 p.

Research output: Contribution to journalArticle

Evolution Equation
Semilinear Evolution Equation
Local Well-posedness
Energy Estimates
Operator
1 Citation (Scopus)

The stokes equation in the Lp-setting: Well-posedness and regularity properties

Hieber, M. G. & Saal, J., 2018 Apr 19, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer International Publishing, p. 117-206 90 p.

Research output: Chapter in Book/Report/Conference proceedingChapter

Regularity Properties
Stokes Equations
regularity
Well-posedness
Stokes

Time periodic and almost time periodic solutions to rotating stratified fluids subject to large forces

Hieber, M. G., Mahalov, A. & Takada, R., 2018 Jan 1, (Accepted/In press) In : Journal of Differential Equations.

Research output: Contribution to journalArticle

Stratified Fluid
Rotating Fluid
Time-periodic Solutions
Buoyancy
Fluids
2017

Bounded H-calculus for the hydrostatic stokes operator on Lp-spaces and applications

Giga, Y., Gries, M., Hieber, M. G., Hussein, A. & Kashiwabara, T., 2017, In : Proceedings of the American Mathematical Society. 145, 9, p. 3865-3876 12 p.

Research output: Contribution to journalArticle

Stokes Operator
Primitive Equations
Hydrostatics
Mixed Boundary Conditions
Lp Spaces
1 Citation (Scopus)

On periodic and almost periodic solutions to incompressible viscous fluid flow problems on the whole line

Hieber, M. G., Nguyen, T. H. & Seyfert, A., 2017 Jan 1, Mathematics for Nonlinear Phenomena—Analysis and Computation - In Honor of Yoshikazu Giga’s 60th Birthday. Springer New York LLC, Vol. 215. p. 51-81 31 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Almost Periodic Solution
Almost Periodic
Viscous Flow
Viscous Fluid
Incompressible Fluid

Preface

Bothe, D., Denk, R., Hieber, M. G., Schnaubelt, R., Simonett, G., Wilke, M. & Zacher, R., 2017 Mar 1, In : Journal of Evolution Equations. 17, 1

Research output: Contribution to journalEditorial

1 Citation (Scopus)

Strong time-periodic solutions to the 3D primitive equations subject to arbitrary large forces

Galdi, G. P., Hieber, M. G. & Kashiwabara, T., 2017 Sep 18, In : Nonlinearity. 30, 10, p. 3979-3992 14 p.

Research output: Contribution to journalArticle

primitive equations
Primitive Equations
Time-periodic Solutions
periodic functions
time functions
2016
13 Citations (Scopus)

A General Approach to Time Periodic Incompressible Viscous Fluid Flow Problems

Geissert, M., Hieber, M. G. & Nguyen, T. H., 2016 Jun 1, In : Archive for Rational Mechanics and Analysis. 220, 3, p. 1095-1118 24 p.

Research output: Contribution to journalArticle

Viscous Flow
Incompressible Flow
Viscous Fluid
Incompressible Fluid
Fluid Flow
7 Citations (Scopus)

Bounded analyticity of the stokes semigroup on spaces of bounded functions

Hieber, M. G. & Maremonti, P., 2016, Recent Developments of Mathematical Fluid Mechanics. Springer Verlag, Vol. none. p. 275-289 15 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

15 Citations (Scopus)

Dynamics of nematic liquid crystal flows: The quasilinear approach

Hieber, M. G., Nesensohn, M., Pruss, J. & Schade, K., 2016 Mar 1, In : Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis. 33, 2, p. 397-408 12 p.

Research output: Contribution to journalArticle

Nematic liquid crystals
Nematic Liquid Crystal
Strong Solution
Dynamics (theory)
Parabolic Equation
3 Citations (Scopus)

Dynamics of the Ericksen–Leslie equations with general Leslie stress I: the incompressible isotropic case

Hieber, M. G. & Prüss, J., 2016 Aug 2, (Accepted/In press) In : Mathematische Annalen. p. 1-20 20 p.

Research output: Contribution to journalArticle

Topology
Local Solution
Stress Tensor
Nematic Liquid Crystal
Strong Solution
3 Citations (Scopus)

Global strong Lp well-posedness of the 3D primitive equations with heat and salinity diffusion

Hieber, M., Hussein, A. & Kashiwabara, T., 2016 Dec 15, In : Journal of Differential Equations. 261, 12, p. 6950-6981 32 p.

Research output: Contribution to journalArticle

Primitive Equations
Salinity
Well-posedness
Interpolation
Heat
9 Citations (Scopus)

Global Strong Well-Posedness of the Three Dimensional Primitive Equations in Lp -Spaces

Hieber, M. G. & Kashiwabara, T., 2016 Sep 1, In : Archive for Rational Mechanics and Analysis. 221, 3, p. 1077-1115 39 p.

Research output: Contribution to journalArticle

Primitive Equations
Lp Spaces
Well-posedness
Hydrostatics
Strong Solution

Strong solutions for two-phase free boundary problems for a class of non-Newtonian fluids

Hieber, M. G. & Saito, H., 2016 Sep 19, (Accepted/In press) In : Journal of Evolution Equations. p. 1-24 24 p.

Research output: Contribution to journalArticle

Non-Newtonian Fluid
Free Boundary Problem
Strong Solution
Stress Tensor
Class
5 Citations (Scopus)

Thermodynamical consistent modeling and analysis of nematic liquid crystal flows

Hieber, M. G. & Prüss, J., 2016, Mathematical Fluid Dynamics, Present and Future. Springer New York LLC, Vol. 183. p. 433-459 27 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Nematic Liquid Crystal
Strong Solution
Leslie model
Dynamics (theory)
Modeling
2015
1 Citation (Scopus)

Global existence results for the Navier–Stokes equations in the rotational framework in Fourier–Besov spaces

Fang, D., Han, B. & Hieber, M. G., 2015, Operator Theory: Advances and Applications. Springer International Publishing, Vol. 250. p. 199-211 13 p. (Operator Theory: Advances and Applications; vol. 250).

Research output: Chapter in Book/Report/Conference proceedingChapter

Global Existence
Existence Results
Navier-Stokes Equations
Mild Solution
Coriolis Force
5 Citations (Scopus)

Local and global existence results for the Navier-Stokes equations in the rotational framework

Fang, D., Han, B. & Hieber, M. G., 2015 Mar 1, In : Communications on Pure and Applied Analysis. 14, 2, p. 609-622 14 p.

Research output: Contribution to journalArticle

Coriolis force
Local Existence
Global Existence
Navier Stokes equations
Existence Results
5 Citations (Scopus)

Pointwise upper bounds for the solution of the Stokes equation on Lσ∞(Ω) and applications

Bolkart, M. & Hieber, M. G., 2015 Apr 1, In : Journal of Functional Analysis. 268, 7, p. 1678-1710 33 p.

Research output: Contribution to journalArticle

Stokes Equations
Semigroup
Upper bound
Stokes
Denote
14 Citations (Scopus)

Stokes resolvent estimates in spaces of bounded functions

Abe, K., Giga, Y. & Hieber, M. G., 2015 May 1, In : Annales Scientifiques de l'Ecole Normale Superieure. 48, 3, p. 537-559 23 p.

Research output: Contribution to journalArticle

Resolvent Estimates
Stokes
Analytic Semigroup
Stokes Operator
Stokes Equations
2 Citations (Scopus)

The Lp-approach to the fluid-rigid body interaction problem for compressible fluids

Hieber, M. G. & Murata, M., 2015, In : Evolution Equations and Control Theory. 4, 1, p. 69-87 19 p.

Research output: Contribution to journalArticle

Compressible Fluid
Strong Solution
Rigid Body
System of equations
Fluid
2014
1 Citation (Scopus)
Exterior Domain
Strong Solution
Global Existence
Velocity Field
Navier Stokes equations
1 Citation (Scopus)

Stability results for fluids of Oldroyd-B type on exterior domains

Geissert, M., Hieber, M. G. & Huy, N. T., 2014 Sep 24, In : Journal of Mathematical Physics. 55, 9, 091505.

Research output: Contribution to journalArticle

Exterior Domain
Fluid
Analytic Semigroup
fluids
2013
17 Citations (Scopus)

Global existence results for Oldroyd-B fluids in exterior domains: The case of non-small coupling parameters

Fang, D., Hieber, M. G. & Zi, R., 2013 Oct, In : Mathematische Annalen. 357, 2, p. 687-709 23 p.

Research output: Contribution to journalArticle

Oldroyd-B Fluid
Exterior Domain
Global Existence
Existence Results
Global Solution
11 Citations (Scopus)

Lp-theory for strong solutions to fluid-rigid body interaction in Newtonian and generalized Newtonian fluids

Geissert, M., Götze, K. & Hieber, M. G., 2013, In : Transactions of the American Mathematical Society. 365, 3, p. 1393-1439 47 p.

Research output: Contribution to journalArticle

Newtonian Fluid
Strong Solution
Rigid Body
Exponent
Fluid

Remarks on the theory of Oldroyd-B fluids in exterior domains

Hieber, M. G., 2013 Oct, In : Discrete and Continuous Dynamical Systems - Series S. 6, 5, p. 1307-1313 7 p.

Research output: Contribution to journalArticle

Oldroyd-B Fluid
Exterior Domain
Boundary conditions
Fluids
Global Existence
2 Citations (Scopus)

Stochastic stability of the Ekman spiral

Hieber, M. G. & Stannat, W., 2013, In : Annali della Scuola Normale - Classe di Scienze. 12, 1, p. 189-208 20 p.

Research output: Contribution to journalArticle

Stochastic Stability
Navier-Stokes
Martingale
Boundary conditions
Stationary Solutions

Well-posedness results for the navier-stokes equations in the rotational framework

Hieber, M. G. & Monniaux, S., 2013 Nov, In : Discrete and Continuous Dynamical Systems- Series A. 33, 11-12, p. 5143-5151 9 p.

Research output: Contribution to journalArticle

Ill-posedness
Open set
Well-posedness
Dirichlet Boundary Conditions
Navier Stokes equations
2012
3 Citations (Scopus)

Density-dependent incompressible viscous fluid flow subject to linearly growing initial data

Fang, D., Hieber, M. G. & Zhang, T., 2012 Aug, In : Applicable Analysis. 91, 8, p. 1477-1493 17 p.

Research output: Contribution to journalArticle

Viscous Flow
Viscous Fluid
Incompressible Fluid
Navier Stokes equations
Fluid Flow
23 Citations (Scopus)

Global existence results for Oldroyd-B fluids in exterior domains

Hieber, M. G., Naito, Y. & Shibata, Y., 2012 Feb 1, In : Journal of Differential Equations. 252, 3, p. 2617-2629 13 p.

Research output: Contribution to journalArticle

Oldroyd-B Fluid
Exterior Domain
Global Existence
Existence Results
Fluids
20 Citations (Scopus)

Weak Neumann implies Stokes

Geissert, M., Heck, H., Hieber, M. G. & Sawada, O., 2012 Aug, In : Journal fur die Reine und Angewandte Mathematik. 669, p. 75-100 26 p.

Research output: Contribution to journalArticle

Hermann Von Helmholtz
Stokes
Projection
Imply
2011

Preface

Escher, J., Guidotti, P., Hieber, M. G., Mucha, P. B., Prüß, J. W., Shibata, Y., Simonett, G., Walker, C. & Zajaczkowski, W., 2011 Jan 1, In : Progress in Nonlinear Differential Equations and Their Application. 80, p. ix-xii

Research output: Contribution to journalEditorial

7 Citations (Scopus)

The spin-coating process: Analysis of the free boundary value problem

Denk, R., Geissert, M., Hieber, M. G., Saal, J. & Sawada, O., 2011 Jul, In : Communications in Partial Differential Equations. 36, 7, p. 1145-1192 48 p.

Research output: Contribution to journalArticle

Free Boundary Value Problems
Spin coating
Boundary value problems
Coating
Regularity
2010
5 Citations (Scopus)

L -estimates for parabolic systems with VMO-coefficients

Heck, H., Hieber, M. G. & Stavrakidis, K., 2010 Jun, In : Discrete and Continuous Dynamical Systems - Series S. 3, 2, p. 299-309 11 p.

Research output: Contribution to journalArticle

Parabolic Systems
Coefficient
A Priori Estimates
Estimate
Parabolic Equation
18 Citations (Scopus)

Maximal L p - L q -Estimates for the stokes equation: A short proof of solonnikov's theorem

Geissert, M., Hess, M., Hieber, M. G., Schwarz, C. & Stavrakidis, K., 2010 Mar, In : Journal of Mathematical Fluid Mechanics. 12, 1, p. 47-60 14 p.

Research output: Contribution to journalArticle

Sectorial Operator
Stokes Operator
Exterior Domain
Stokes Equations
Bounded Domain
9 Citations (Scopus)

Nonlinear stability of Ekman boundary layers

Hess, M., Hieber, M. G., Mahalov, A. & Saal, J., 2010 Aug, In : Bulletin of the London Mathematical Society. 42, 4, p. 691-706 16 p.

Research output: Contribution to journalArticle

Nonlinear Stability
Boundary Layer
Stationary Solutions
Decay Rate
Half-space
2 Citations (Scopus)

Remarks on the L p-approach to the stokes equation on unbounded domains

Geissert, M., Heck, H., Hieber, M. G. & Sawada, O., 2010 Jun, In : Discrete and Continuous Dynamical Systems - Series S. 3, 2, p. 291-297 7 p.

Research output: Contribution to journalArticle

Stokes Operator
Analytic Semigroup
Stokes Equations
Hermann Von Helmholtz
Unbounded Domain
37 Citations (Scopus)

The Fujita-Kato approach to the Navier-Stokes equations in the rotational framework

Hieber, M. G. & Shibata, Y., 2010 Jun, In : Mathematische Zeitschrift. 265, 2, p. 481-491 11 p.

Research output: Contribution to journalArticle

Mild Solution
Navier-Stokes Equations
Norm
Arbitrary
Framework
2009
12 Citations (Scopus)

Global properties of generalized Ornstein-Uhlenbeck operators on Lp (RN, RN) with more than linearly growing coefficients

Hieber, M. G., Lorenzi, L., Prüss, J., Rhandi, A. & Schnaubelt, R., 2009 Feb 1, In : Journal of Mathematical Analysis and Applications. 350, 1, p. 100-121 22 p.

Research output: Contribution to journalArticle

Ornstein-Uhlenbeck Operator
Lp Estimates
Gradient Estimate
Strongly Continuous Semigroups
Pointwise Estimates
8 Citations (Scopus)
Stokes Flow
Strong Solution
Navier-Stokes
Mild Solution
Rotating
2008
3 Citations (Scopus)

Irreducibility and mixed boundary conditions

Haller-Dintelmann, R., Hieber, M. G. & Rehberg, J., 2008 Feb, In : Positivity. 12, 1, p. 83-91 9 p.

Research output: Contribution to journalArticle

Positive Semigroup
Nonsmooth Domains
Mixed Boundary Conditions
Irreducibility
Neumann Boundary Conditions
24 Citations (Scopus)

Quasilinear parabolic systems with mixed boundary conditions on nonsmooth domains

Hieber, M. G. & Rehberg, J., 2008, In : SIAM Journal on Mathematical Analysis. 40, 1, p. 292-305 14 p.

Research output: Contribution to journalArticle

Quasilinear Parabolic Systems
Nonsmooth Domains
Maximal Regularity
Kernel Estimate
Quasilinear System
2007
1 Citation (Scopus)

Lp-theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle

Geissert, M. & Hieber, M. G., 2007, In : Acta Mathematica Universitatis Comenianae. 76, 1, p. 69-76 8 p.

Research output: Contribution to journalArticle

Stokes Flow
Navier-Stokes
Rotating
111 Citations (Scopus)

Optimal L p -L q -estimates for parabolic boundary value problems with inhomogeneous data

Denk, R., Hieber, M. G. & Prüss, J., 2007 Sep, In : Mathematische Zeitschrift. 257, 1, p. 193-224 32 p.

Research output: Contribution to journalArticle

Boundary Value Problem
Triebel-Lizorkin Space
General Boundary Conditions
Ellipticity
Parabolic Problems
2006
25 Citations (Scopus)

Lp - Lq Estimates for parabolic systems in non-divergence form with VMO coefficients

Haller-Dintelmann, R., Heck, H. & Hieber, M. G., 2006 Dec, In : Journal of the London Mathematical Society. 74, 3, p. 717-736 20 p.

Research output: Contribution to journalArticle

Lp Estimates
Parabolic Systems
Muckenhoupt Weights
Coefficient
Unique Solution
61 Citations (Scopus)

L p-theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle

Geissert, M., Heck, H. & Hieber, M. G., 2006 Jul 1, In : Journal fur die Reine und Angewandte Mathematik. 596, p. 45-62 18 p.

Research output: Contribution to journalArticle

Stokes Flow
Navier-Stokes
Rotating
Navier-Stokes Problem
Stokes Equations

The model-problem associated to the Stefan problem with surface tension: An approach via Fourier-Laplace multipliers

Geissert, M., Grec, B., Hieber, M. G. & Radkevich, E., 2006 Jan 1, Differential Equations: Inverse and Direct Problems. CRC Press, p. 171-182 12 p.

Research output: Chapter in Book/Report/Conference proceedingChapter

Stefan Problem
Laplace
Surface Tension
Multiplier
Model
2005
3 Citations (Scopus)

H ∞-calculus for products of non-commuting operators

Haller-Dintelmann, R. & Hieber, M. G., 2005 Sep, In : Mathematische Zeitschrift. 251, 1, p. 85-100 16 p.

Research output: Contribution to journalArticle

Commutator Estimate
Sectorial Operator
Calculus
Banach space
Operator