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Global solution of the isothermal viscous gas equation in the whole space with a large external force deriving a potential. (Solution globale de l’équation d’un gaz visqueux isotherme dans l’espace entier avec une grande force extérieure dérivant d’un potentiel.) (French) Zbl 0852.35086

The author considers the initial value problem for the system of equations of isothermal viscous gas in the whole space. He shows that the solution of this initial value problem exists uniquely globally in time. First, he proves the existence and uniqueness of a solution of the initial value problem for a linearized system of equations. Then the existence and uniqueness of a local (in time) solution for the initial value problem for a viscous gas system of equations is proved. Some estimates of this local solution are given too.
Reviewer: V.A.Sava (Iaşi)

MSC:

35L15 Initial value problems for second-order hyperbolic equations
35Q35 PDEs in connection with fluid mechanics
76N15 Gas dynamics (general theory)
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References:

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