| Bemerkung |
This lecture concerns the regularity of abstract (linear) Cauchy problems on abstract Banach spaces that generalize linear parabolic PDEs such as the heat equation. We investigate the exact time-space regularity of solutions depending on the forcing term. We will first start by considering evolution equations in Hilbert spaces. Eventually, we investigate the foundation of L^q-maximal regularity theory in the general framework. Finally, we provide applications to nonlinear PDEs including existence and uniqueness results for the nonlinear heat equation as well as incompressible Navier-Stokes. |
