Communications in Mathematical Sciences
Volume 13 (2015)
Wild solutions for 2D incompressible ideal flow with passive tracer
Pages: 1333 – 1343
In [C. De Lellis and L. Székelyhidi, Ann. of Math. (2), 170(3), 1417–1436, 2009], 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.
weak solutions, wild solutions, incompressible MHD
2010 Mathematics Subject Classification
35D30, 35Q35, 76B03, 76W05