Navier-Stokes equation regzlarity
of weak solutions A
Meyers' type estimate for weak solutions to a generalized
Pierre-Etienne Druet Druet
Pierre-Etienne
Joachim Naumann Naumann
Joachim
Jörg Wolf Wolf
Jörg
Institut
für Mathematik, Humboldt-Universität zu Berlin (ISSN
0863-0976), 2008-6
Pierre-Etienne Druet
, Joachim Naumann
, Jörg Wolf
Preprint series: Institut für Mathematik,
Humboldt-Universität zu Berlin (ISSN 0863-0976), 2008-6
MSC 2000
- 35Q30 Stokes and Navier-Stokes equations
- 35D10 Regularity of generalized solutions
Abstract
In
this paper, we prove a Meyers' type estimate for weak solutions to a
Stokes system with bounded measurable coefficients in place of the
usual constant viscosity. Besides the perturbation argument due to
Meyers, we make use of the solvability of the classical Stokes problem
in $[ W^{ 1,\, q}_{0,\sigma } (\Omega )]^n\, (n=2 \,\, \mbox{or}
\,\,n=3, 2< q < 3+\var, \partial \Omega \,\, \mbox{Lipschitz} ).
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