Global solution of the isothermal viscous gas equation in the whole space with a large external force deriving a potential
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.
scientific article; zbMATH DE number 889842
scientific article