Global and local existence for the dissipative critical SQG equation\n with small oscillations

2013/08/04 by Omar Lazar, Lazar, Omar · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1308.0851

openalex publication_date 2013/08/04 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

This article is devoted to the study of the critical dissipative surface\nquasi-geostrophic (SQG) equation in \ℝ². For any initial data\n\θ₀ belonging to the space \Λ^s ( H^s_uloc(\ℝ²))\n\∩ L^\∞(\ℝ²), we show that the critical (SQG) equation has at\nleast one global weak solution in time for all 1/4\≤ s \≤ 1/2 and at\nleast one local weak solution in time for all 0<s<1/4. The proof for the\nglobal existence is based on a new energy inequality which improves the one\nobtain in citeLaz whereas the local existence uses more refined energy\nestimates based on Besov space techniques.\n

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