# zbMATH — the first resource for mathematics

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)
Full Text: