3 years ago

A note on regularity of the pressure in the Navier–Stokes system

Sanja Friganović

Abstract

In this note we improve the standard regularity of the dynamic part of the pressure in the Navier–Stokes system. Using the theory of elliptic equations with \(L^1\) right-hand side we prove that, in addition to be in \(L^2\) , the dynamic pressure belongs to \(W^{1,\alpha }_{loc} \) with \(1<\alpha <\frac{n}{n-1}\) , in case of Dirichlet boundary condition. For pressure boundary condition the dynamic pressure is proved to be in \(W^{1,\alpha } \) . As a consequence, for the force \(\mathbf{f} \in L^q (\Omega )^n \) and \(q>n /2 \) the pressure turns out to be continuous.

Publisher URL: https://link.springer.com/article/10.1007/s11565-018-0302-x

DOI: 10.1007/s11565-018-0302-x

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