Dynamical Systems Seminar

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Maximal regularity estimates for evolutionary systems

Speaker: Sebastian Król, Adam Mickiewicz University in Poznan

Location: Warren Weaver Hall 705

Date: Wednesday, December 4, 2024, 3:15 p.m.

Synopsis:

Motivated by recent applications of end-point maximal regularity estimates to the study of strong/classical, global-in-time well-posedness for various problems arising in fluid mechanics (such as the Stokes system), we will review Da Prato-Grisvard-type results, which are central to these applications, in connection with the maximum regularity theory of parabolic evolution equations. After a brief discussion of the basic concepts and illustrative evolutionary systems, we will present an extension of Da Prato-Grisvard theory that has new and noteworthy implications for the solvability of such systems.