Communications in Mathematical Sciences

Volume 13 (2015)

Number 5

Wild solutions for 2D incompressible ideal flow with passive tracer

Pages: 1333 – 1343

(Fast Communication)

DOI: http://dx.doi.org/10.4310/CMS.2015.v13.n5.a12

Authors

Anne C. Bronzi (Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, Cidade Universitária, Campinas, SP, Brazil)

Milton C. Lopes Filho (Instituto de Matemática, Universidade Federal do Rio de Janeiro, Cidade Universitária, Ilha do Fundão, Rio de Janeiro, RJ, Brazil)

Helena J. Nussenzveig Lopes (Instituto de Matemática, Universidade Federal do Rio de Janeiro, Cidade Universitária, Ilha do Fundão, Rio de Janeiro, RJ, Brazil)

Abstract

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.

Keywords

weak solutions, wild solutions, incompressible MHD

2010 Mathematics Subject Classification

35D30, 35Q35, 76B03, 76W05

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