Beale-Kato-Majda type condition for Burgers equation

2008/02/19 by Beniamin Gołdys, Ben Goldys, Goldys, Ben +2
Engineering · Mathematics · Physics and Astronomy · #35Q35 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math-ph #math.AP #math.MP #msc:35Q35

paper · pdf · doi:10.48550/arxiv.0802.2733

21 pages, accepted to "Journal of mathematical analysis and applications"

openalex publication_date 2008/02/19 · arxiv created 2008/12/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a multidimensional Burgers equation on the torus \mathbbT^d and the whole space \Rd. We show that, in case of the torus, there exists a unique global solution in Lebesgue spaces. For a torus we also provide estimates on the large time behaviour of solutions. In the case of \Rd we establish the existence of a unique global solution if a Beale-Kato-Majda type condition is satisfied. To prove these results we use the probabilistic arguments which seem to be new.

Citations

• StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions
• Shocklike Dynamics of Inelastic Gases

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