@inproceedings{9099023e8fd445b49029d368f944f944,

title = "Regularity of weak solutions for the Navier-Stokes equations via energy criteria",

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) ∥22 or the dissipation energy ∫ t 0 ∥∇u(τ ) ∥2 2 dτ is (left-side) H{\"o}lder continuous as a function of time t with H{\"o}lder exponent 1/2 and with sufficiently small H{\"o}lder 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 = "Energy criteria, H{\"o}lder continuity, Navier-Stokes equations, Regularity criteria, Weak solutions",

author = "Reinhard Farwig and Hideo Kozono and Hermann Sohr",

note = "Copyright: Copyright 2021 Elsevier B.V., All rights reserved.; 2007 International Conference on Mathematical Fluid Mechanics ; Conference date: 21-05-2007 Through 25-05-2007",

year = "2010",

doi = "10.1007/978-3-642-04068-9_13",

language = "English",

isbn = "9783642040672",

series = "Advances in Mathematical Fluid Mechanics - Dedicated to Giovanni Paolo Galdi on the Occasion of His 60th Birthday",

publisher = "Springer Verlag",

pages = "215--227",

booktitle = "Advances in Mathematical Fluid Mechanics - Dedicated to Giovanni Paolo Galdi on the Occasion of His 60th Birthday",

}