On Expansion of Regularity of Nonlinear ...
Type de document :
Pré-publication ou Document de travail
Titre :
On Expansion of Regularity of Nonlinear Evolution Equations by Means of Dilation Symmetry
Auteur(s) :
Mot(s)-clé(s) en anglais :
Nonlinear Evolution Equations
Dilation Symmetry
Dilation Symmetry
Discipline(s) HAL :
Mathématiques [math]/Systèmes dynamiques [math.DS]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Résumé en anglais : [en]
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 ...
Lire la suite >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.Lire moins >
Lire la suite >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.Lire moins >
Langue :
Anglais
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