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Existence of a weak solution to the Navier–Stokes equation in a general time-varying domain by the Rothe method

✍ Scribed by Jiří Neustupa

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
343 KB
Volume
32
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We assume that Ω^t^ is a domain in ℝ^3^, arbitrarily (but continuously) varying for 0⩽t⩽T. We impose no conditions on smoothness or shape of Ω^t^. We prove the global in time existence of a weak solution of the Navier–Stokes equation with Dirichlet's homogeneous or inhomogeneous boundary condition in Q~[0, T)~ := {(x, t);0⩽t⩽T, x∈Ω^t^}. The solution satisfies the energy‐type inequality and is weakly continuous in dependence of time in a certain sense. As particular examples, we consider flows around rotating bodies and around a body striking a rigid wall. Copyright © 2008 John Wiley & Sons, Ltd.

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