On the initial value problem for the Navier-Stokes equations with the initial datum in the Sobolev spaces

D. Q. Khai, V. T. T. Duong

In this paper, we study local well-posedness for the Navier-Stokes equations with arbitrary initial data in homogeneous Sobolev spaces ${\dot{H}}_p^s({\mathbb{R}}^d)$ for $d \geq 2, p…