TY - JOUR
T1 - Vorticity Measures and the Inviscid Limit
AU - Constantin, Peter
AU - Lopes Filho, Milton C.
AU - Nussenzveig Lopes, Helena J.
AU - Vicol, Vlad
N1 - Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/11/1
Y1 - 2019/11/1
N2 - We consider a sequence of Leray-Hopf weak solutions of the 2D Navier-Stokes equations on a bounded domain, in the vanishing viscosity limit. We provide sufficient conditions on the associated vorticity measures, away from the boundary, which ensure that as the viscosity vanishes the sequence converges to a weak solution of the Euler equations. The main assumptions are local interior uniform bounds on the L1-norm of vorticity and the local uniform convergence to zero of the total variation of vorticity measure on balls, in the limit of vanishing ball radii.
AB - We consider a sequence of Leray-Hopf weak solutions of the 2D Navier-Stokes equations on a bounded domain, in the vanishing viscosity limit. We provide sufficient conditions on the associated vorticity measures, away from the boundary, which ensure that as the viscosity vanishes the sequence converges to a weak solution of the Euler equations. The main assumptions are local interior uniform bounds on the L1-norm of vorticity and the local uniform convergence to zero of the total variation of vorticity measure on balls, in the limit of vanishing ball radii.
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U2 - 10.1007/s00205-019-01398-1
DO - 10.1007/s00205-019-01398-1
M3 - Article
AN - SCOPUS:85067033980
SN - 0003-9527
VL - 234
SP - 575
EP - 593
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 2
ER -