New entropy for Korteweg's system, existence of global weak solution and Prodi-Serrin theorem
Haspot, Boris (2011), New entropy for Korteweg's system, existence of global weak solution and Prodi-Serrin theorem. https://basepub.dauphine.fr/handle/123456789/7227
TypeDocument de travail / Working paper
External document linkhttp://arxiv.org/abs/1102.5436v1
Basque Center of Applied Mathematics
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Abstract (EN)This work is devoted to prove new entropy estimates for a general isothermal model of capillary fluids derived by J.E Dunn and J.Serrin (1985) (see ), which can be used as a phase transition model. More precisely we will derive new estimates for the density and we will give a new structure for the Korteweg system which allow us to obtain the existence of global weak solution. The key of the proof comes from the introduction of a new effective velocity.The proof is widely inspired from the works of A. Mellet and A. Vasseur (see ). In a second part, we shall give a Prody-Serrin blow-up criterion for this system which widely improves the results of  and the known results on compressible systems.
Subjects / KeywordsProdi-Serrin theorem; Weak solutions; entropy; Korteweg system
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Existence of global strong solution and vanishing capillarity-viscosity limit in one dimension for the Korteweg system Haspot, Boris; Charve, Frédéric (2013) Article accepté pour publication ou publié
Existence of global strong solution for Korteweg system in one dimension for strongly degenerate viscosity coefficients Burtea, Cosmin; Haspot, Boris (2022) Article accepté pour publication ou publié