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 paperExternal document link
http://arxiv.org/abs/1102.5436v1Date
2011Publisher
Basque Center of Applied Mathematics
Published in
Derio (Espagne)
Pages
28
Metadata
Show full item recordAuthor(s)
Haspot, BorisAbstract (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 systemRelated items
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