The Australian Journal of Mathematical Analysis and Applications

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Paper's Title:

Existence and Estimate of the Solution for the Approximate Stochastic Equation to the Viscous Barotropic Gas


R. Benseghir and A. Benchettah

LANOS Laboratory,
Badji Mokhtar University,
PO Box 12,
Annaba, Algeria.


A stochastic equation of a viscous barotropic gas is considered. The application of Ito formula to a specific functional in an infinite dimensional space allows us to obtain an estimate which is useful to analyse the behavior of the solution. As it is difficult to exploit this estimate, we study an approximate problem. More precisely, we consider the equation of a barotropic viscous gas in Lagrangian coordinates and we add a diffusion of the density. An estimate of energy is obtained to analyse the behavior of the solution for this approximate problem and Galerkin method is used to prove the existence and uniqueness of the solution.

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