Solvability of the free boundary value problem of the Navier-Stokes equations | Zendy

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Solvability of the free boundary value problem of the Navier-Stokes equations

Author(s) -

Hantaek Bae

Publication year - 2010

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2011.29.769

Subject(s) - bounded function , sobolev space , domain (mathematical analysis) , mathematics , navier–stokes equations , mathematical analysis , boundary value problem , free boundary problem , compressibility , vector field , free surface , boundary (topology) , physics , geometry , mechanics

In this paper, we study the incompressible Navier-Stokes equations on a moving domain in R(3) of finite depth, bounded above by the free surface and bounded below by a solid flat bottom. We prove that there exists a unique, global-in-time solution to the problem provided that the initial velocity field and the initial profile of the boundary are sufficiently small in Sobolev spacesclose11

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