Maximal Regularity and Partial Differential Equations

The theory of maximal regularity is a powerful tool to get solutions having the best regularity to linear partial differential equations (PDEs) of parabolic type. The theory is also applicable to show well-posedness of various non-linear PDEs.

In the first part, We introduce the history of the development of the theory of maximal regularity and the way to apply non-linear PDEs.

In the second part, We give some applications to PDEs, e. g. the primitive equations, the Navier-Stokes equations, and elliptic equations with dynamic boundary conditions.

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