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 proceedingConference contribution

1 Citation (Scopus)

Abstract

Consider a weak solution u of the instationary Navier-Stokes system in a bounded domain of R3 satisfying the strong energy inequality. Extending previous results by Farwig et al., J. Math. Fluid Mech. 11, 1-14 (2008), we prove among other things that u is regular if either the kinetic energy 1/2 ∥u(t) ∥2 2 or the dissipation energy ∫ t 0 ∥∇u(τ ) ∥2 2 dτ is (left-side) Hölder continuous as a function of time t with Hölder exponent 1/2 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
Pages215-227
Number of pages13
DOIs
Publication statusPublished - 2010
Externally publishedYes
Event2007 International Conference on Mathematical Fluid Mechanics - Estoril
Duration: 2007 May 212007 May 25

Other

Other2007 International Conference on Mathematical Fluid Mechanics
CityEstoril
Period07/5/2107/5/25

Fingerprint

Navier Stokes equations
Kinetic energy
Energy dissipation
Fluids

Keywords

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

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes

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) 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. 2010. p. 215-227.

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

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, 2007 International Conference on Mathematical Fluid Mechanics, Estoril, 07/5/21. 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. 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. 2010. pp. 215-227
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