For any >0 we show the existence of continuous periodic weak solutions v of the Euler equations that do not conserve the kinetic energy and belong to the space Lt1(Cx1/3-epsilon); namely, x?v (x,t) is 1/3-epsilon-Holder continuous in space at a.e. time t and the integral displaystyle="true">[upsilon(,t)]1/3-epsilon dt is finite. A well-known open conjecture of L. Onsager claims that such solutions exist even in the class Lt(Cx1/3-epsilon).
Dissipative Euler Flows with Onsager-Critical Spatial Regularity
De Lellis, C.;
2016-01-01
Abstract
For any >0 we show the existence of continuous periodic weak solutions v of the Euler equations that do not conserve the kinetic energy and belong to the space Lt1(Cx1/3-epsilon); namely, x?v (x,t) is 1/3-epsilon-Holder continuous in space at a.e. time t and the integral displaystyle="true">[upsilon(,t)]1/3-epsilon dt is finite. A well-known open conjecture of L. Onsager claims that such solutions exist even in the class Lt(Cx1/3-epsilon).File in questo prodotto:
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