TY - GEN

T1 - Regularity of weak solutions for the Navier-Stokes equations via energy criteria

AU - Farwig, Reinhard

AU - Kozono, Hideo

AU - Sohr, Hermann

PY - 2010/12/1

Y1 - 2010/12/1

N2 - 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) 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.

AB - 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) 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.

KW - Energy criteria

KW - Hölder continuity

KW - Navier-Stokes equations

KW - Regularity criteria

KW - Weak solutions

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U2 - 10.1007/978-3-642-04068-9-13

DO - 10.1007/978-3-642-04068-9-13

M3 - Conference contribution

AN - SCOPUS:84896762645

SN - 9783642040672

T3 - Advances in Mathematical Fluid Mechanics - Dedicated to Giovanni Paolo Galdi on the Occasion of His 60th Birthday

SP - 215

EP - 227

BT - Advances in Mathematical Fluid Mechanics - Dedicated to Giovanni Paolo Galdi on the Occasion of His 60th Birthday

T2 - 2007 International Conference on Mathematical Fluid Mechanics

Y2 - 21 May 2007 through 25 May 2007

ER -