In this paper addresses the initial value problem for the Navier-Stokes equations in Rm (m = 2; 3;..) with initial condition in the subspace PLp(Rm) of Lp(Rm), characterized by the null divergence condition. The problem is studied considering its integral formulation, where an argument of successive approximations is used. The existence and uniqueness of the local solution is proven depending on a condition of smallness in the time of existence. On the other hand, the overall result is tested with a small amount of the initial data.

In this paper addresses the initial value problem for the Navier-Stokes equations in Rm (m = 2; 3;..) with initial condition in the subspace PLp(Rm) of Lp(Rm), characterized by the null divergence condition. The problem is studied considering its integral formulation, where an argument of successive approximations is used. The existence and uniqueness of the local solution is proven depending on a condition of smallness in the time of existence. On the other hand, the overall result is tested with a small amount of the initial data.