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Archiv der Mathematik

, Volume 112, Issue 6, pp 661–672 | Cite as

Well-posedness to 3D Burgers’ equation in critical Gevrey Sobolev spaces

  • Ridha SelmiEmail author
  • Abdelkerim Châabani
Article
  • 10 Downloads

Abstract

We prove that the three-dimensional periodic Burgers’ equation has a unique global in time solution in a critical Gevrey–Sobolev space. Comparatively to Navier–Stokes equations, the main difficulty is the lack of an incompressibility condition. In our proof of existence, we overcome the bootstrapping argument, which was a technical step in a precedent proof in Sololev spaces. This makes our proof shorter and gives sense of considering the Gevrey class for a mathematical study to Burgers’ equation. To prove that the unique solution is global in time, we use the maximum principle. Energy methods, Sobolev product laws, compactness methods, and Fourier analysis are the main tools.

Keywords

Burgers’ equation Critical Gevrey–Sobolev space Existence Uniqueness Global solution 

Mathematics Subject Classification

Primary 35A01 35A02 Secondary 35B10 35B50 

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Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics College of ScienceNorthern Border UniversityArarKingdom of Saudi Arabia
  2. 2.Department of Mathematics Faculty of Mathematical, Physical and Natural Sciences of TunisUniversity of Tunis El ManarTunisTunisia

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