Solonnikov, V. A. 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 Zap. Nauchn. Semin. POMI 197, 159-178 (1992). 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. Cited in 1 Review MSC: 76D05 Navier-Stokes equations for incompressible viscous fluids 35Q30 Navier-Stokes equations Keywords:unique generalized solution; finite time interval; small initial and boundary data; vector fields; infinite energy integral PDFBibTeX XMLCite \textit{V. A. Solonnikov}, Zap. Nauchn. Semin. POMI 197, 159--178 (1992; Zbl 0773.76025) Full Text: EuDML