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arXiv · 1009.4024

On the flux problem in the theory of steady Navier-Stokes equations with nonhomogeneous boundary conditions

Mikhail V. Korobkov·Konstantin Pileckas·Remigio Russo
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Abstract

We study the nonhomogeneous boundary value problem for Navier--Stokes equations of steady motion of a viscous incompressible fluid in a two--dimensional bounded multiply connected domain $Ω=Ω_1\setminus\barΩ_2, \;\barΩ_2\subset Ω_1$. We prove that this problem has a solution if the flux $\F$ of the boundary value through $\partialΩ_2$ is nonnegative. The proof of the main result uses the Bernoulli law for a weak solution to the Euler equations and the one-side maximum principle for the total head pressure corresponding to this solution.

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Mikhail V. Korobkov, Konstantin Pileckas, Remigio Russo. 2011-10-28. On the flux problem in the theory of steady Navier-Stokes equations with nonhomogeneous boundary conditions. https://arxiv.org/abs/1009.4024

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