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


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Article Info

DATE

2019-03-19

AUTHORS

Ridha Selmi, Abdelkerim Châabani

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. More... »

PAGES

1-12

References to SciGraph publications

  • 2016-12. On the Blow-up Criterion of 3D-NSE in Sobolev–Gevrey Spaces in JOURNAL OF MATHEMATICAL FLUID MECHANICS
  • 1972-01. The initial value problem for the Navier-Stokes equations with data in Lp in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
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    http://scigraph.springernature.com/pub.10.1007/s00013-019-01303-y

    DOI

    http://dx.doi.org/10.1007/s00013-019-01303-y

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