Strong solutions to compressible-incompressible two-phase flows with phase transitions

Keiichi Watanabe

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arXiv · 1808.07241

Strong solutions to compressible-incompressible two-phase flows with phase transitions

Keiichi Watanabe

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Abstract

We consider a free boundary problem of compressible-incompressible two-phase flows with phase transitions in general domains of $N$-dimensional Euclidean space (e.g. whole space; half-spaces; bounded domains; exterior domains). The compressible fluid and the incompressible fluid are separated by either compact or non-compact sharp moving interface, and the surface tension is taken into account. In our model, the compressible fluid and incompressible fluid are occupied by the Navier-Stokes-Korteweg equations and the Navier-Stokes equations, respectively. This paper shows that for given $T > 0$ the problem admits a unique strong solution on $(0,T)$ in the maximal $L_p - L_q$ regularity class provided the initial data are small in their natural norms.

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Keiichi Watanabe. 2018-08-22. Strong solutions to compressible-incompressible two-phase flows with phase transitions. https://arxiv.org/abs/1808.07241

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