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The Navier-Stokes equation in noncylindrical domain. (English) Zbl 0895.35076
Summary: We study the existence of weak solutions to the Navier-Stokes equation defined in a noncylindrical domain \[ \widehat Q=\cup_{0\leq t\leq T} \Omega_t \times\{t\}, \quad \Omega_t= \bigl\{K(t)y, y\in\Omega \bigr\},\;\Omega\subset \mathbb{R}^n, \] and \(\widehat Q\) is not necessarily increasing or decreasing in time. Regularity and uniqueness of solutions for the case \(n=2\) are also considered.

MSC:
35Q30 Navier-Stokes equations
35D05 Existence of generalized solutions of PDE (MSC2000)
35D10 Regularity of generalized solutions of PDE (MSC2000)
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