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On Expansion of Regularity of Nonlinear Evolution Equations by Means of Dilation Symmetry

Andrey Polyakov 1
1 VALSE - Finite-time control and estimation for distributed systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : The paper present a dilation symmetry based approach to expansion of regularity of nonlinear evolution equations. In particular, it is shown that a symmetry of an operator, which describes a right-hand side of a non-linear evolution equation, is inherited by solutions of this equation. In the case of dilation symmetry, the latter implies that global-in-time existence of solutions for small initial data always imply global-in-time existence of solutions for large initial data. As an example, we consider the problem of expansion of regularity of the Navier-Stokes equations (in $\R^n$) accepting that the existence of global-in-time solutions for small initial data is already proven.
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https://hal.inria.fr/hal-02093984
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Submitted on : Thursday, May 2, 2019 - 4:34:48 PM
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Andrey Polyakov. On Expansion of Regularity of Nonlinear Evolution Equations by Means of Dilation Symmetry. 2019. ⟨hal-02093984v2⟩

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