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arXiv · 0902.0965

Existence of weak solution for compressible fluid models of Korteweg type

Boris Haspot
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Abstract

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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Boris Haspot. 2009-02-05. Existence of weak solution for compressible fluid models of Korteweg type. https://doi.org/10.1007/s00021-009-0013-2

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