Regularity of weak solutions for the Navier-Stokes equations via energy criteria

Reinhard Farwig, Hideo Kozono, Hermann Sohr

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

Abstract

Consider a weak solution u of the instationary Navier-Stokes system in a bounded domain of satisfying the strong energy inequality. Extending previous results Farwig et al., Journal of Mathematical Fluid Mechanics, 2007, to appear we prove among other things that u is regular if either the kinetic energy or the dissipation energy is (left-side) HÖlder continuous as a function of time t with HÖlder exponent and with sufficiently small HÖlder seminorm. The proofs use local regularity results which are based on the theory of very weak solutions and on uniqueness arguments for weak solutions.

Original languageEnglish
Title of host publicationAdvances in Mathematical Fluid Mechanics: Dedicated to Giovanni Paolo Galdi on the Occasion of his 60th Birthday
PublisherSpringer Berlin Heidelberg
Pages215-227
Number of pages13
ISBN (Print)9783642040672
DOIs
Publication statusPublished - 2010
Externally publishedYes

Fingerprint

Weak Solution
Navier-Stokes Equations
Regularity
Very Weak Solutions
Energy Inequality
Seminorm
Navier-Stokes System
Fluid Mechanics
Energy Dissipation
Energy
Kinetic energy
Thing
Bounded Domain
Uniqueness
Exponent

Keywords

  • Energy criteria
  • Hölder continuity
  • Navier-Stokes equations
  • Regularity criteria
  • Weak solutions

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Farwig, R., Kozono, H., & Sohr, H. (2010). Regularity of weak solutions for the Navier-Stokes equations via energy criteria. In Advances in Mathematical Fluid Mechanics: Dedicated to Giovanni Paolo Galdi on the Occasion of his 60th Birthday (pp. 215-227). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-04068-9_13

Regularity of weak solutions for the Navier-Stokes equations via energy criteria. / Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann.

Advances in Mathematical Fluid Mechanics: Dedicated to Giovanni Paolo Galdi on the Occasion of his 60th Birthday. Springer Berlin Heidelberg, 2010. p. 215-227.

Research output: Chapter in Book/Report/Conference proceedingChapter

Farwig, R, Kozono, H & Sohr, H 2010, Regularity of weak solutions for the Navier-Stokes equations via energy criteria. in Advances in Mathematical Fluid Mechanics: Dedicated to Giovanni Paolo Galdi on the Occasion of his 60th Birthday. Springer Berlin Heidelberg, pp. 215-227. https://doi.org/10.1007/978-3-642-04068-9_13
Farwig R, Kozono H, Sohr H. Regularity of weak solutions for the Navier-Stokes equations via energy criteria. In Advances in Mathematical Fluid Mechanics: Dedicated to Giovanni Paolo Galdi on the Occasion of his 60th Birthday. Springer Berlin Heidelberg. 2010. p. 215-227 https://doi.org/10.1007/978-3-642-04068-9_13
Farwig, Reinhard ; Kozono, Hideo ; Sohr, Hermann. / Regularity of weak solutions for the Navier-Stokes equations via energy criteria. Advances in Mathematical Fluid Mechanics: Dedicated to Giovanni Paolo Galdi on the Occasion of his 60th Birthday. Springer Berlin Heidelberg, 2010. pp. 215-227
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