B Haspot
Published 2011-02-26Version 1
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 \cite{fDS}), 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 \cite{fMV}). In a second part, we shall give a Prody-Serrin blow-up criterion for this system which widely improves the results of \cite{Hprepa} and the known results on compressible systems.
Global weak solution to the viscous two-phase model with finite energy
On the nonexistence of global weak solutions to the Navier-Stokes-Poisson equations in $\Bbb R^N$
Large data limit for a phase transition model with the p-Laplacian on point clouds
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