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Global Well-Posedness of a Non-local Burgers Equation: the Periodic Case

Abstract : This paper is concerned with the study of a non-local Burgers equation for positive bounded periodic initial data. The equation reads u_t − u|∇|u + |∇|(u^2) = 0. We construct global classical solutions starting from smooth positive data, and global weak solutions starting from data in L ∞. We show that any weak solution is instantaneously regularized into C ∞. We also describe the long-time behavior of all solutions. Our methods follow several recent advances in the regularity theory of parabolic integro-differential equations.
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https://hal.archives-ouvertes.fr/hal-01160752
Contributor : Francois Vigneron <>
Submitted on : Sunday, June 7, 2015 - 10:39:24 AM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM
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  • HAL Id : hal-01160752, version 1
  • ARXIV : 1506.02240

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Cyril Imbert, Roman Shvydkoy, Francois Vigneron. Global Well-Posedness of a Non-local Burgers Equation: the Periodic Case. Annales de la Faculté des Sciences de Toulouse. Mathématiques., Université Paul Sabatier _ Cellule Mathdoc 2016, 25 (4), pp.723-758. ⟨hal-01160752⟩

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