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On the use of tent spaces for solving PDEs: A proof of the Koch-Tataru theorem

On the use of tent spaces for solving PDEs: A proof of the Koch-Tataru theorem

In these notes we will present (a part of) the parabolic tent spaces theory and then apply it in solving some PDE's originated from the fluid mechanics. In more details, to our most interest are the incompressible homogeneous Navier-Stokes equations. These equations have been investigated mathematically for almost one century. …