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Global existence of solutions of the Dirichlet problem for the compressible Navier‐Stokes equations
Author(s) -
Mucha P.B.,
Zaja̧czkowski W.M.
Publication year - 2004
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310080
Subject(s) - mathematics , compressibility , dirichlet problem , dirichlet boundary condition , domain (mathematical analysis) , mathematical analysis , navier–stokes equations , dirichlet distribution , boundary value problem , boundary (topology) , physics , mechanics
We prove the existence of global in time regular solutions of the compressible Navier‐Stokes equations in a domain Ω ⊂ R 3 with vanishing Dirichlet boundary conditions. The solutions are close to nontrivial static solutions. A key element of the proof is a special L p ‐estimate for the linearized problem to show that the velocity belongs to W 2,1 r (loc) (Ω × [0,∞)) with r > 3 which is the sharp result in this approach.