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Research Output 1987 2019

  • 2546 Citations
  • 29 h-Index
  • 156 Article
  • 3 Conference contribution
  • 2 Editorial
  • 1 Chapter
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Article
2007
6 Citations (Scopus)

Global solutions of semirelativistic hartree type equations

Cho, Y. & Ozawa, T., 2007 Sep, In : Journal of the Korean Mathematical Society. 44, 5, p. 1065-1078 14 p.

Research output: Contribution to journalArticle

Global Solution
Global Existence
Initial Value Problem
Convolution
Scattering
41 Citations (Scopus)

On small amplitude solutions to the generalized boussinesq equations

Cho, Y. & Ozawa, T., 2007 Apr, In : Discrete and Continuous Dynamical Systems. 17, 4, p. 691-711 21 p.

Research output: Contribution to journalArticle

Boussinesq Equations
Modified Equations
Generalized Equation
Scattering
Term
2006
4 Citations (Scopus)

Global existence on nonlinear Schrödinger-IMBq equations

Cho, Y. & Ozawa, T., 2006, In : Journal of Mathematics of Kyoto University. 46, 3, p. 535-552 18 p.

Research output: Contribution to journalArticle

Blow-up Criterion
Global Existence
Nonlinearity
BMO Space
Triebel-Lizorkin Space
4 Citations (Scopus)

On a decay property of solutions to the Haraux-Weissler equation

Fukuizumi, R. & Ozawa, T., 2006 Feb 1, In : Journal of Differential Equations. 221, 1, p. 134-142 9 p.

Research output: Contribution to journalArticle

Weighted Sobolev Spaces
Variational Approach
Weight Function
Decay
Sobolev spaces
47 Citations (Scopus)

On the semirelativistic Hartree-type equation

Cho, Y. & Ozawa, T., 2006, In : SIAM Journal on Mathematical Analysis. 38, 4, p. 1060-1074 15 p.

Research output: Contribution to journalArticle

Scattering Problems
Asymptotic Behavior of Solutions
Nonexistence
Cauchy Problem
Infinity
11 Citations (Scopus)
Boussinesq Equations
Modified Equations
One Dimension
Cauchy
Nonexistence
41 Citations (Scopus)
Gauge Invariance
Control nonlinearities
Invariance
Nonlinear equations
Conservation Laws
2005
12 Citations (Scopus)

Analytic smoothing effect for solutions to schrödinger equations with nonlinearity of integral type

Ozawa, T., Yamauchi, K. & Yamazaki, Y., 2005 Dec, In : Osaka Journal of Mathematics. 42, 4, p. 737-750 14 p.

Research output: Contribution to journalArticle

Smoothing Effect
Nonlinearity
Exponential Type
Cauchy
Cauchy Problem
55 Citations (Scopus)

Endpoint Strichartz estimates and global solutions for the nonlinear Dirac equation

Machihara, S., Nakamura, M., Nakanishi, K. & Ozawa, T., 2005 Feb 1, In : Journal of Functional Analysis. 219, 1, p. 1-20 20 p.

Research output: Contribution to journalArticle

Strichartz Estimates
Global Well-posedness
Polar coordinates
Klein-Gordon Equation
Dirac Equation
10 Citations (Scopus)

Exponential decay of solutions to nonlinear elliptic equations with potentials

Fukuizumi, R. & Ozawa, T., 2005 Nov, In : Zeitschrift fur Angewandte Mathematik und Physik. 56, 6, p. 1000-1011 12 p.

Research output: Contribution to journalArticle

Decay of Solutions
Nonlinear Elliptic Equations
Exponential Decay
Harmonic Potential
Decay Estimates
4 Citations (Scopus)

Sharp asymptotic behavior of solutions to nonlinear Schrödinger equations with repulsive interactions

Kita, N. & Ozawa, T., 2005 Apr, In : Communications in Contemporary Mathematics. 7, 2, p. 167-176 10 p.

Research output: Contribution to journalArticle

Large Time Behavior
Asymptotic Behavior of Solutions
Nonlinear equations
Cauchy Problem
Nonlinear Equations
2004
6 Citations (Scopus)

On solutions of the wave equation with homogeneous Cauchy data

Kato, J. & Ozawa, T., 2004 Feb, In : Asymptotic Analysis. 37, 2, p. 93-107 15 p.

Research output: Contribution to journalArticle

Wave equations
Cauchy
Wave equation
Propagation of Singularities
Self-similar Solutions
3 Citations (Scopus)
Smoothing Effect
Large Time Behavior
Behavior of Solutions
Nonlinearity
Interaction
4 Citations (Scopus)

Weighted Strichartz estimates for the wave equation in even space dimensions

Kato, J. & Ozawa, T., 2004 Aug, In : Mathematische Zeitschrift. 247, 4, p. 747-764 18 p.

Research output: Contribution to journalArticle

Strichartz Estimates
Weighted Estimates
Wave equation
Odd
Huygens' Principle
2003
87 Citations (Scopus)

Interpolation inequalities in Besov spaces

Machihara, S. & Ozawa, T., 2003 May, In : Proceedings of the American Mathematical Society. 131, 5, p. 1553-1556 4 p.

Research output: Contribution to journalArticle

Interpolation Inequality
Besov Spaces
Homogeneous Space
Interpolation
11 Citations (Scopus)

Life-span of smooth solutions to the complex Ginzburg-Landau type equation on a torus

Ozawa, T. & Yamazaki, Y., 2003 Nov, In : Nonlinearity. 16, 6, p. 2029-2034 6 p.

Research output: Contribution to journalArticle

Integral Means
life span
Complex Ginzburg-Landau Equation
Landau-Ginzburg equations
Ginzburg-Landau
36 Citations (Scopus)

Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation

Machihara, S., Nakanishi, K. & Ozawa, T., 2003, In : Revista Matematica Iberoamericana. 19, 1, p. 179-194 16 p.

Research output: Contribution to journalArticle

Non-relativistic Limit
Dirac Equation
Global Solution
Nonlinear Equations
Strichartz Estimates
9 Citations (Scopus)

Weighted Strichartz Estimates and Existence of Self-similar Solutions for Semilinear Wave Equations

Kato, J. & Ozawa, T., 2003, In : Indiana University Mathematics Journal. 52, 6, p. 1615-1630 16 p.

Research output: Contribution to journalArticle

Strichartz Estimates
Weighted Estimates
Semilinear Wave Equation
Self-similar Solutions
Odd
2002
1 Citation (Scopus)
Global Solution
Nonlinear Schrödinger Equation
Nonlinearity
60 Citations (Scopus)

Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations

Machihara, S., Nakanishi, K. & Ozawa, T., 2002, In : Mathematische Annalen. 322, 3, p. 603-621 19 p.

Research output: Contribution to journalArticle

Non-relativistic Limit
Nonlinear Klein-Gordon Equation
Optimal Rate of Convergence
Energy
Cauchy Problem
44 Citations (Scopus)

Remarks on scattering for nonlinear Schrödinger equations

Nakanishi, K. & Ozawa, T., 2002, In : Nonlinear Differential Equations and Applications. 9, 1, p. 45-68 24 p.

Research output: Contribution to journalArticle

Sobolev spaces
Nonlinear equations
Nonlinear Equations
Scattering
Maximal Regularity
2001

Small solutions to nonlinear wave equations in the Sobolev spaces

Nakamura, M. & Ozawa, T., 2001, In : Houston Journal of Mathematics. 27, 3, p. 613-632 20 p.

Research output: Contribution to journalArticle

Small Solutions
Global Well-posedness
Nonlinear Wave Equation
Sobolev Spaces
Homogeneous Space
38 Citations (Scopus)

The Cauchy Problem for Nonlinear Klein-Gordon Equations in the Sobolev Spaces

Nakamura, M. & Ozawa, T., 2001, In : Publications of the Research Institute for Mathematical Sciences. 37, 3, p. 255-293 39 p.

Research output: Contribution to journalArticle

Nonlinear Klein-Gordon Equation
Global Well-posedness
Sobolev Spaces
Cauchy Problem
Exponential Growth
2000
10 Citations (Scopus)

Small solutions to nonlinear Schrödinger equations in the Sobolev spaces

Nakamura, M. & Ozawa, T., 2000, In : Journal d'Analyse Mathematique. 81, p. 305-329 25 p.

Research output: Contribution to journalArticle

Small Solutions
Global Well-posedness
Sobolev Spaces
Nonlinear Equations
Fractional Order
1999
29 Citations (Scopus)

Global solutions in the critical Sobolev space for the wave equations with nonlinearity of exponential growth

Nakamura, M. & Ozawa, T., 1999 Jul, In : Mathematische Zeitschrift. 231, 3, p. 479-487 9 p.

Research output: Contribution to journalArticle

Exponential Growth
Global Solution
Sobolev Spaces
Wave equation
Nonlinearity
12 Citations (Scopus)

The Cauchy problem for nonlinear wave equations in the sobolev space of critical order

Nakamura, M. & Ozawa, T., 1999 Jan, In : Discrete and Continuous Dynamical Systems. 5, 1, p. 215-231 17 p.

Research output: Contribution to journalArticle

Sobolev spaces
Exponential Type
Nonlinear Wave Equation
Wave equations
Sobolev Spaces
44 Citations (Scopus)

Well-posedness in energy space for the Cauchy problem of the Klein-Gordon-Zakharov equations with different propagation speeds in three space dimensions

Ozawa, T., Tsutaya, K. & Tsutsumi, Y., 1999 Jan, In : Mathematische Annalen. 313, 1, p. 127-140 14 p.

Research output: Contribution to journalArticle

Propagation Speed
Klein-Gordon Equation
Well-posedness
Cauchy Problem
Energy
1998
68 Citations (Scopus)

Nonlinear Schrödinger Equations in the Sobolev Space of Critical Order

Nakamura, M. & Ozawa, T., 1998 Jun 1, In : Journal of Functional Analysis. 155, 2, p. 364-380 17 p.

Research output: Contribution to journalArticle

Sobolev Spaces
Nonlinear Equations
Exponential Type
Interaction
Cauchy
25 Citations (Scopus)

Scattering theory for the Hartree equation

Hayashi, N., Naumkin, P. I. & Ozawa, T., 1998 Sep, In : SIAM Journal on Mathematical Analysis. 29, 5, p. 1256-1267 12 p.

Research output: Contribution to journalArticle

Hartree Equation
Scattering Theory
Scattering Problems
Scattering
1997
33 Citations (Scopus)

Low energy scattering for nonlinear Schrödinger equations in fractional order Sobolev spaces

Nakamura, M. & Ozawa, T., 1997 Apr, In : Reviews in Mathematical Physics. 9, 3, p. 397-410 14 p.

Research output: Contribution to journalArticle

Sobolev space
Fractional Order
norms
Sobolev Spaces
nonlinear equations
1996
13 Citations (Scopus)

Dilation method and smoothing effects of solutions to the Benjamin-Ono equation

Hayashi, N., Kato, K. & Ozawa, T., 1996, In : Royal Society of Edinburgh - Proceedings A. 126, 2, p. 273-285 13 p.

Research output: Contribution to journalArticle

Benjamin-Ono Equation
Smoothing Effect
Hilbert Transform
Dilation
58 Citations (Scopus)

Global existence and asymptotic behavior of solutions for the Klein-Gordon equations with quadratic nonlinearity in two space dimensions

Ozawa, T., Tsutaya, K. & Tsutsumi, Y., 1996 Jul, In : Mathematische Zeitschrift. 222, 3, p. 341-362 22 p.

Research output: Contribution to journalArticle

Klein-Gordon Equation
Asymptotic Behavior of Solutions
Global Existence
Nonlinearity
85 Citations (Scopus)

On the nonlinear Schrödinger equations of derivative type

Ozawa, T., 1996 Mar, In : Indiana University Mathematics Journal. 45, 1, p. 137-163 27 p.

Research output: Contribution to journalArticle

Cauchy Problem
Nonlinear Equations
Derivative
Wave Operator
Global Well-posedness
1995
12 Citations (Scopus)

Global, small radially symmetric solutions to nonlinear Schrödinger equations and a gauge transformation

Hayashi, N., Ozawa, T. & Temam, R., 1995, In : Differential and Integral Equations. 8, 5, p. 1061-1072 12 p.

Research output: Contribution to journalArticle

Radially Symmetric Solutions
Gauge Transformation
Energy Method
Nonlinear equations
Global Existence
106 Citations (Scopus)

On Critical Cases of Sobolev′s Inequalities

Ozawa, T., 1995 Feb 1, In : Journal of Functional Analysis. 127, 2, p. 259-269 11 p.

Research output: Contribution to journalArticle

Critical Case
Alternatives
Form
1994
55 Citations (Scopus)

Modified wave operators for the derivative nonlinear Schrödinger equation

Hayashi, N. & Ozawa, T., 1994 Jan, In : Mathematische Annalen. 298, 1, p. 557-576 20 p.

Research output: Contribution to journalArticle

Wave Operator
Nonlinear Schrödinger Equation
Derivative
81 Citations (Scopus)

Remarks on nonlinear Schrödinger equations in one space dimension

Hayashi, N., Ozawa, T. & Bona, J. L., 1994, In : Differential and Integral Equations. 7, 2, p. 453-461 9 p.

Research output: Contribution to journalArticle

Initial value problems
Local Solution
Nonlinear equations
Initial Value Problem
Nonlinear Equations

Wave propagation in even-dimensional spaces

Ozawa, T., 1994 Aug, In : Asymptotic Analysis. 9, 2, p. 163-176 14 p.

Research output: Contribution to journalArticle

Wave equations
Wave propagation
Wave Propagation
Cones
Fourier transforms
1993
113 Citations (Scopus)

Long range scattering for non-linear Schrödinger and Hartree equations in space dimension n≥2

Ginibre, J. & Ozawa, T., 1993 Feb, In : Communications in Mathematical Physics. 151, 3, p. 619-645 27 p.

Research output: Contribution to journalArticle

Hartree Equation
Nonlinear Equations
Scattering
Wave Operator
Scattering Problems
1992
28 Citations (Scopus)

Nonlinear scattering with nonlocal interaction

Nawa, H. & Ozawa, T., 1992 May, In : Communications in Mathematical Physics. 146, 2, p. 259-275 17 p.

Research output: Contribution to journalArticle

Nonlocal Interactions
Wave Operator
Scattering
operators
Scattering Problems
98 Citations (Scopus)

On the derivative nonlinear Schrödinger equation

Hayashi, N. & Ozawa, T., 1992, In : Physica D: Nonlinear Phenomena. 55, 1-2, p. 14-36 23 p.

Research output: Contribution to journalArticle

Sobolev space
Sobolev spaces
Nonlinear equations
nonlinear equations
Nonlinear Equations
38 Citations (Scopus)

The nonlinear Schrödinger limit and the initial layer of the Zakharov equations

Ozawa, T., Tsutsumi, Y. & Brezis, H., 1992, In : Differential and Integral Equations. 5, 4, p. 721-745 25 p.

Research output: Contribution to journalArticle

Convergence of Solutions
Nonlinear equations
Convergence Rate
Nonlinear Equations
Infinity
1991
151 Citations (Scopus)

Long range scattering for nonlinear Schrödinger equations in one space dimension

Ozawa, T., 1991 Aug, In : Communications in Mathematical Physics. 139, 3, p. 479-493 15 p.

Research output: Contribution to journalArticle

Wave Operator
nonlinear equations
Nonlinear Equations
Scattering
Sobolev space
15 Citations (Scopus)

Non-existence of wave operators for Stark effect Hamiltonians

Ozawa, T., 1991 May, In : Mathematische Zeitschrift. 207, 1, p. 335-339 5 p.

Research output: Contribution to journalArticle

Wave Operator
Nonexistence
5 Citations (Scopus)

Space-time behavior of propagators for Schrödinger evolution equations with Stark effect

Ozawa, T., 1991 May 1, In : Journal of Functional Analysis. 97, 2, p. 264-292 29 p.

Research output: Contribution to journalArticle

Propagator
Evolution Equation
Electric Field
Space-time
61 Citations (Scopus)
Mixed Problem
Schrödinger
Weak Solution
Uniqueness
1990

Non-existence of positive commutators

Ozawa, T., 1990, In : Hiroshima Mathematical Journal. 20, 1, p. 209-211 3 p.

Research output: Contribution to journalArticle

Commutator
Nonexistence
1 Citation (Scopus)

Relative bounds of closable operators in non-reflexive Banach spaces

Kozono, H. & Ozawa, T., 1990, In : Hokkaido Mathematical Journal. 19, 2, p. 241-248 8 p.

Research output: Contribution to journalArticle

Banach space
Operator
8 Citations (Scopus)

Smoothing effects and dispersion of singularities for the Schrödinger evolution group

Ozawa, T., 1990 May, In : Archive for Rational Mechanics and Analysis. 110, 2, p. 165-186 22 p.

Research output: Contribution to journalArticle

Smoothing Effect
Wave functions
Regularity
Singularity
Decay
6 Citations (Scopus)
Stokes Flow
Navier-Stokes
n-dimensional
Bounded Domain