Nonlinear open mapping principles, with applications to the Jacobian and the incompressible Euler equations
I will present a nonlinear version of the open mapping principle which applies to scale-invariant constant-coefficient PDEs which are preserved under weak* convergence. As a first application, I will consider the prescribed Jacobian equation, explaining the relation of our result with a long-standing problem by Coifman, Lions, Meyer and Semmes. As a second application, the incompressible Euler equations will be considered, showing that a Baire-generic initial datum does not admit dissipative solutions. This talk is based on joint work with Lukas Koch (Oxford) and Sauli Lindberg (Aalto).
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