Existence of Global Weak Solution for Compressible Fluid Models of Korteweg Type
Haspot, Boris (2011), Existence of Global Weak Solution for Compressible Fluid Models of Korteweg Type, Journal of Mathematical Fluid Mechanics, 13, 2, p. 223-249. http://dx.doi.org/10.1007/s00021-009-0013-2
TypeArticle accepté pour publication ou publié
External document linkhttp://arxiv.org/abs/0902.0965v1
Journal nameJournal of Mathematical Fluid Mechanics
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Abstract (EN)This work is devoted to proving existence of global weak solutions for a general isothermal model of capillary fluids derived by Dunn and Serrin (Arch Rational Mech Anal 88(2):95–133, 1985) which can be used as a phase transition model. We improve the results of Danchin and Desjardins (Annales de l’IHP, Analyse non linéaire 18:97–133, 2001) 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 κ. 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.
Subjects / Keywordscompactness and concentration; gain of derivability; Weak solutions
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Porous media equations, fast diffusion equations and the existence of global weak solution for the quasi-solution of compressible Navier-Stokes equations Haspot, Boris (2014) Communication / Conférence
From the Highly Compressible Navier–Stokes Equations to Fast Diffusion and Porous Media Equations. Existence of Global Weak Solution for the Quasi-Solutions Haspot, Boris (2016) Article accepté pour publication ou publié