# Oberwolfach Seminar: Introduction to convex integration

created by modena on 04 Mar 2020

31 may 2020 - 6 jun 2020   [open in google calendar]

Mathematisches Forschungsinstitut Oberwolfach

Convex integration is a technique for the construction of solutions to certain nonlinear systems of partial differential equations. The technique originates in the work of John Nash 1954 on $C^1$ isometric embeddings and has been developed into a powerful general method in Gromov’s book for certain problems in differential geometry.

In the last decade new versions of this technique have been developed primarily for applications in fluid mechanics. Most notable achievements are (1) the non-uniqueness of weak solutions to the incompressible Euler system and to the p-system of compressible ideal flows; (2) the resolution of Onsager’s conjecture on anomalous dissipation in the context of the K41 theory of turbulence; (3) the non-uniqueness of distributional solutions of the Navier-Stokes equations and of distributional solutions of the linear transport equation with Sobolev vector fields.

The lectures aim to provide an exposition to these separate achievements and to address the corresponding developments at the forefront of this still emerging theory.

The seminar takes place at the Mathematisches Forschungsinstitut Oberwolfach. The Institute covers board and lodging. By the support of the Carl Friedrich von Siemens Foundation travel expenses can be reimbursed up to 150 EUR in average per person (against copies of travel receipts). The number of participants is restricted to 25.

Organizers: Daniel Faraco, Stefano Modena, László Jr Székelyhidi.

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