Unique solvability of a two-dimensional nonstationary problem for the convection equations with temperature-dependent viscosity
The global motion of a drop of a viscous compressible heat conducting fluid is considered. Assuming that the initial data are sufficiently close to an equilibrium state and the external force, the heat sources and the heat flow through the boundary vanish, the authors prove the existence of a global in time solution to the appropriate equations which is close to the equilibrium state for any moment of time. They rewrite the main equations in Lagrangian coordinates in order to formulate the local existence theorem, and apply the method of successive approximations to prove the local existence. To prove the global existence of the solutions, they obtain fine estimates and consider appropriate compatibility conditions on the boundary.
viscous compressible heat conducting fluid
scientific article; zbMATH DE number 1916032