Large time regular solutions to the Navier-Stokes equations in cylindrical domains
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Navier-Stokes equations, motions in cylindrical domains, boundary slip conditions, global existence of regular solutions, large dataAbstrakt
We prove the large time existence of solutions to the Navier-Stokes equations with slip boundary conditions in a cylindrical domain. Assuming smallness of $L_2$-norms of derivatives of initial velocity with respect to variable along the axis of the cylinder, we are able to obtain estimate for velocity in $W^{2,1}_2$ without restriction on its magnitude. Then existence follows from the Leray-Schauder fixed point theorem.Pobrania
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2008-09-01
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RENCŁAWOWICZ, Joanna & ZAJĄCZKOWSKI, Wojciech M. Large time regular solutions to the Navier-Stokes equations in cylindrical domains. Topological Methods in Nonlinear Analysis [online]. 1 wrzesień 2008, T. 32, nr 1, s. 69–87. [udostępniono 3.7.2024].
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