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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

Type
Document de travail / Working paper
External document link
http://arxiv.org/abs/1102.5436v1
Date
2011
Publisher
Basque Center of Applied Mathematics
Published in
Derio (Espagne)
Pages
28
Metadata
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Author(s)
Haspot, Boris
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 [14]), 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 [33]). In a second part, we shall give a Prody-Serrin blow-up criterion for this system which widely improves the results of [17] and the known results on compressible systems.
Subjects / Keywords
Prodi-Serrin theorem; Weak solutions; entropy; Korteweg system

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