Existence of weak solution for compressible fluid models of Korteweg type

Details Existence of weak solution for compressible fluid models of Korteweg type Existence of weak solution for compressible fluid models of Korteweg type

2009-02-05

arxiv.org/abs/0902.0965v1

Mathematics

Analysis of PDEs

Scientific paper

This work is devoted to prove existence of global weak solutions for a general isothermal model of capillary fluids derived by J.- E Dunn and J. Serrin (1985) [6], which can be used as a phase transition model. We improve the results of [5] by showing the existence of global weak solution in dimension two for initial data in the energy space, close to a stable equilibrium and with specific choices on the capillary coefficients. In particular we are interested in capillary coefficients approximating a constant capillarity coefficient. To finish we show the existence of global weak solution in dimension one for a specific type of capillary coefficients with large initial data in the energy space.

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