Regularity of Weak Solutions for the Navier-Stokes Equations Via Energy Criteria

Reinhard Farwig (), Hideo Kozono () and Hermann Sohr ()
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Reinhard Farwig: Darmstadt University of Technology, Department of Mathematics
Hideo Kozono: Tähoku University, Mathematical Institute
Hermann Sohr: University of Paderborn, Faculty of Computer Science, Electrical Engineering and Mathematics

A chapter in Advances in Mathematical Fluid Mechanics, 2010, pp 215-227 from Springer

Abstract: 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.

Keywords: Navier-Stokes equations; Weak solutions; Regularity criteria; Energy criteria; Hölder continuity (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-04068-9_13

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DOI: 10.1007/978-3-642-04068-9_13

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