Système de gaz sans pression avec viscosité et diffusion non linéaire

Translated title of the contribution: Pressureless gas equations with viscosity and nonlinear diffusion

Azzouz Dermoune, Boualem Djehiche

Research output: Contribution to journalArticlepeer-review


Under some regularity conditions on P0 and u0, we derive a unique local strong solution of the following system of pressureless gas equations with viscosity: ∂Pt∂t+div(uPt)=σ22ΔP t,∂(uPt)∂t+div(u2P t)=σ22Δ(uPt),P t→P0,uPt→u0P 0,weakly, ast→0+, by constructing a nonlinear diffusion process as solution to the following SDE: Xt=X0+∫0tE[u0(X0)X s]ds+σBt,L(X0)=P0. We show then that Pt is the probability density of Xt while the velocity field admits the following stochastic representation: u(t,x)=E[u0(X0)Xt=x].

Translated title of the contributionPressureless gas equations with viscosity and nonlinear diffusion
Original languageFrench
Pages (from-to)745-750
Number of pages6
JournalComptes Rendus de l'Academie des Sciences - Series I: Mathematics
Issue number8
StatePublished - Apr 15 2001

ASJC Scopus subject areas

  • General Mathematics


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