Examines the initial value problem for non-stationary Stokes flows, under a non-linear boundary conditions which can be called the leak boundary condition of friction type. Examination of the solvability of the initia...Examines the initial value problem for non-stationary Stokes flows, under a non-linear boundary conditions which can be called the leak boundary condition of friction type. Examination of the solvability of the initial value problem; Methods of analysis; Review of non-linear semigroup theory.展开更多
The time-dependent Navier-Stokes equations with leak boundary conditions are investigated in this paper. The equivalent variational inequality is derived, and the weak and strong solvabilities of this variational ineq...The time-dependent Navier-Stokes equations with leak boundary conditions are investigated in this paper. The equivalent variational inequality is derived, and the weak and strong solvabilities of this variational inequality are obtained by the Galerkin approximation method and the regularized method. In addition, the continuous dependence property of solutions on given initial data is establisbed, from which the strong solution is unique.展开更多
文摘Examines the initial value problem for non-stationary Stokes flows, under a non-linear boundary conditions which can be called the leak boundary condition of friction type. Examination of the solvability of the initial value problem; Methods of analysis; Review of non-linear semigroup theory.
基金Supported by the National Natural Science Foundation of China(No.50306019,No.10571142,No.10471110,No.10471109)
文摘The time-dependent Navier-Stokes equations with leak boundary conditions are investigated in this paper. The equivalent variational inequality is derived, and the weak and strong solvabilities of this variational inequality are obtained by the Galerkin approximation method and the regularized method. In addition, the continuous dependence property of solutions on given initial data is establisbed, from which the strong solution is unique.
