Existence and uniqueness of a regular solution of the Cauchy-Dirichlet problem for the equation of turbulent filtration
In studies of water infiltration through a porous medium in the case of turbulent flows the classical Darcy's law ceases to be true because of large velocities. The flow is described by the equation of turbulent filtration, derived from the continuity equation and from a nonclassical Darcy's law. The aim of this paper is to prove the existence and uniqueness of a regular solution of the Cauchy-Dirichlet problem for turbulent filtration. The term ``regular solution'' means that this solution is Hölder continuous and can be represented as a limit of solutions of some regularized problems. Inner and boundary weighted gradient estimates for the regular solution are established.
water infiltration through a porous medium
inner and boundary weighted gradient estimates
scientific article; zbMATH DE number 1541252
scientific article