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arXiv · 1910.09854

The $\mathcal{R}-$bounded operator families arising from the study of the barotropic compressible flows with free surface

Xin Zhang
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Abstract

In this paper, we study some model problem associated to the free boundary value problem of the barotropic compressible Navier-Stokes equations in general smooth domain with taking surface tension into account. To obtain the maximal $L_p-L_q$ regularity property of the model problem, we prove the existence of $\mathcal{R}-$bounded operator families of the resolvent problem via Weis' theory on operator valued Fourier multipliers.

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Xin Zhang. 2019-10-22. The $\mathcal{R}-$bounded operator families arising from the study of the barotropic compressible flows with free surface. https://arxiv.org/abs/1910.09854

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