Weak solution for compressible fluid models of Korteweg type

Details Weak solution for compressible fluid models of Korteweg type Weak solution for compressible fluid models of Korteweg type

2008-03-13

arxiv.org/abs/0803.1925v1

Mathematics

Analysis of PDEs

Scientific paper

This work is devoted to proving existence of global weak solutions for a general isothermal model of capillary fluids derived by J.E Dunn and J.Serrin (1985) \cite{3DS}, which can be used as a phase transition model. We distinguish two cases when the dimension N=2 and N=1, in the first case we need that $\frac{1}{\rho}\in L^{\infty}$, when N=1 we get a weak solution in finite time in the energy space.

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