Global existence of solutions of the Dirichlet problem for the compressible Navier‐Stokes equations | Zendy

Mucha P.B. | Zendy; Zaja̧czkowski W.M. | Zendy

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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.

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