Seminar Analysis and Mathematical Physics: Vikram Giri (ETH Zürich)

Newton-Nash iterations in PDE

A common issue in convex integration methods (going back to Nash) is the presence of unwanted high-high frequency interactions. These issues can prevent the methods from producing solutions with the optimum "Onsager" regularity to a given system of PDEs. We will discuss these issues in the setting of the 2D Euler equations and then discuss a linear Newton iteration designed to get rid of these unwanted interactions in this setting. We will conclude by discussing applications to other PDEs. This is based on joint works with Răzvan-Octavian Radu and Mimi Dai.

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