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Dissipative Euler Flows with Onsager-Critical Spatial Regularity
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DOI：10.1002/cpa.21586.png)
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Abstract
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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).(c) 2016 Wiley Periodicals, Inc.
Keywords:
INCOMPRESSIBLE EULER
WEAK SOLUTIONS
ENERGY-CONSERVATION
CONJECTURE
EQUATIONS
FLUID
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