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

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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Dates and versions

hal-02093984 , version 1 (09-04-2019)
hal-02093984 , version 2 (02-05-2019)

Identifiers

  • HAL Id : hal-02093984 , version 2

Cite

Andrey Polyakov. On Expansion of Regularity of Nonlinear Evolution Equations by Means of Dilation Symmetry. 2019. ⟨hal-02093984v2⟩
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