On the maximal space analyticity radius for the 3D Navier–Stokes equations and energy cascades |
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Authors: | Animikh Biswas Ciprian Foias |
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Institution: | 1. Department of Mathematics and Statistics, University of North Carolina-Charlotte, 9201 Univ. City. Blvd, Charlotte, NC, 28223, USA 2. Department of Mathematics, Texas A&M University, Mailstop 3368, College Station, TX, 77843, USA
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Abstract: | In this paper, we study the maximal space analyticity radius associated with a regular solution of the Navier–Stokes equations and its connection to turbulence. In order to do this, we introduce a new auxiliary ODE for the evolution of the analyticity radius involving the Gevrey class norms. We further show that jumps in the maximal space analyticity radius are an intermittent event and are connected to inverse energy cascade. Our approach also leads to a new type of global regularity test for the Navier–Stokes equation. |
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