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

Reinhard Farwig, Hideo Kozono, Hermann Sohr

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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.

元の言語English
ホスト出版物のタイトルAdvances in Mathematical Fluid Mechanics
ホスト出版物のサブタイトルDedicated to Giovanni Paolo Galdi on the Occasion of his 60th Birthday
出版者Springer Berlin Heidelberg
ページ215-227
ページ数13
ISBN(印刷物)9783642040672
DOI
出版物ステータスPublished - 2010 12 1

ASJC Scopus subject areas

  • Mathematics(all)

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    Farwig, R., Kozono, H., & Sohr, H. (2010). 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 (pp. 215-227). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-04068-9_13