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arXiv · 1610.03956

Local existence of smooth solutions to multiphase models in two space dimensions

Roberta Bianchini·Roberto Natalini
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Abstract

In this paper, we consider a class of models for multiphase fluids, in the framework of mixture theory. The considered system, in its more general form, contains both the gradient of a hydrostatic pressure, generated by an incompressibility constraint, and the gradient of a compressible pressure depending on the volume fractions of some of the different phases. To approach these systems, we define an approximation based on the \emph{Leray} projection, which involves the use of the \emph{Lax} symbolic symmetrizer for hyperbolic systems and paradifferential techniques. In two space dimensions, we prove its well-posedness and convergence to the unique classical solution to the original system. In the last part, we shortly discuss the difficulties in the three dimensional case.

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Roberta Bianchini, Roberto Natalini. 2016-10-13. Local existence of smooth solutions to multiphase models in two space dimensions. https://arxiv.org/abs/1610.03956

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