Show simple item record

dc.contributor.authorHaspot, Boris
dc.descriptionProceedings of the HYP2012 International Conferencedevoted to Theory, Numerics and Applications of Hyperbolic Problems,Padova, June 24{29, 2012
dc.subjectWeak solutions
dc.subjectNavier–Stokes equations
dc.titlePorous media equations, fast diffusion equations and the existence of global weak solution for the quasi-solution of compressible Navier-Stokes equations
dc.typeCommunication / Conférence
dc.description.abstractenWe have developed a new tool called \textit{quasi solutions} which approximate in some sense the compressible Navier-Stokes equation. In particular it allows us to obtain global strong solution for the compressible Navier-Stokes equations with \textit{large} initial data on the irrotational part of the velocity (\textit{large} in the sense that the smallness assumption is subcritical in terms of scaling, it turns out that in this framework we are able to obtain large initial data in the energy space in dimension $N=2$). In this paper we are interested in proving the result anounced in \cite{cras3} concerning the existence of global weak solution for the quasi-solutions, we also observe that for some choice of initial data (irrotationnal) the quasi solutions verify the porous media, the heat equation or the fast diffusion equations in function of the structure of the viscosity coefficients. In particular it implies that exists classical quasi-solutions in the sense that they are $C^{\infty}$ on $(0,T)\times\R^{N}$ for any $T>0$. Finally we show the convergence of the global weak solution of compressible Navier-Stokes equations to the quasi solutions in the case of a vanishing pressure limit. In particular we show that for highly compressible equations the speed of propagation of the density is quasi finite when the viscosity corresponds to $\mu(\rho)=\rho^{\alpha}$ with $\alpha>1$ and that the density is not far from converging asymptoticaly to the Barrenblatt solution of mass the initial density $\rho_{0}$.
dc.relation.ispartoftitleHyperbolic Problems: Theory, Numerics, Applications
dc.relation.ispartofeditorFabio Ancona, Alberto Bressan, Pierangelo Marcati, Andrea Marson

Files in this item


There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record