Norm Inflation For The Critical SQG Equation

2025/12/09 by Guo, Dengjun, Luo, Xiaoyutao
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.08816

Abstract

We consider the critical dissipative surface quasi-geostrophic (SQG) equation on ℝ² or \mathbbT². Despite global regularity of the equation, we show that the data-to-solution map at the critical level H¹ is not uniformly bounded. We construct solutions that experience H¹ norm inflation from smooth, compactly supported initial data with large H¹ norm. We also demonstrate small-data norm inflation in supercritical Sobolev spaces W^β,p for 1

Citations

• Instantaneous continuous loss of Sobolev regularity for the 3D incompressible Euler equation
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Related

• Global and local existence for the dissipative critical SQG equation\n with small oscillations
• Global well-posedness of slightly supercritical SQG equations and gradient estimate
• On the global regularity for the supercritical SQG equation
• Sharp norm inflation for 3D Navier-Stokes equations in supercritical spaces
• Global well-posedness for supercritical SQG with perturbations of radially symmetric data