UNIQUE STRONG SOLVABILITY OF THE INITIAL BOUNDARY VALUE PROBLEM FOR THE INHOMOGENEOUS INCOMPRESSIBLE KELVIN–VOIGT FLUID MODEL

The paper proves the existence and uniqueness theorem of a strong solution for a inhomogeneous incompressible Kelvin-Voigt fluid motion model. It is not assumed that the initial condition for the fluid density is separated from zero. To prove the existence of a solution, an approximation problem is considered, its solvability and strong a priori estimates for its solutions, independent of the approximation parameter, are established. After that, a passage to the limit is carried out as the approximation parameter tends to zero and it is shown that solutions to the approximation problem converge to a strong solution of the original problem as the approximation parameter tends to zero. The uniqueness of the solution is established using the Gronwall–Bellman inequality.

existence theorem, uniqueness theorem, regularity of solution, inhomogeneous incompressible fluid, Kelvin–Voigt model, a priori estimate model