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On the initial-boundary value problem for the Navier-Stokes equations with discontinuous boundary conditions in the case of two spatial variables. (Russian. English summary) Zbl 0773.76025

Summary: We consider initial-boundary value problem for the Navier-Stokes equations with boundary conditions \(\vec v|_{\partial\Omega}=\vec a\) assuming that \(\vec a\) may have jump discontinuities at a finite number of points \(\xi_ 1,\dots,\xi_ m\) of the boundary \(\partial\Omega\) of a bounded domain \(\Omega\subset\mathbb{R}^ 2\). It is proved that this problem possesses a unique generalized solution in a finite time interval or for small initial and boundary data. The solution is found in a class of vector fields with an infinite energy integral. The case of moving boundary is also considered.

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
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