Wild solutions for 2D incompressible ideal flow with passive tracer

Abstract

In Ann. Math., 170 (2009), 1417-1436, C. De Lellis and L. Székelyhidi Jr. constructed wild solutions of the incompressible Euler equations using a reformulation of the Euler equations as a differential inclusion together with convex integration. In this article we adapt their construction to the system consisting of adding the transport of a passive scalar to the two-dimensional incompressible Euler equations.

10 pages

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