On the uniqueness of the quasi-geostrophic equation with the fractional Laplacian

2025/04/30 by Tsukasa Iwabuchi, Iwabuchi, Tsukasa, Taiki Okazaki +1
Mathematics · Earth and Planetary Sciences · #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Aquatic and Environmental Studies

paper · pdf · doi:10.48550/arxiv.2504.21257

Abstract

We consider the uniqueness of the solution of the surface quasi-geostrophic equation with fractional Laplacian. We show that the uniqueness holds in non-homogeneous Besov spaces without any additional assumption which is supposed to constract solutions. When the power of the fractional Laplacian is close to 2, we prove that the uniqueness with the regularity index s=-1/2. We extract the least regularity s=-1/2 for the well-definedness of the nonlinear term of the equation.

Citations

• On the uniqueness of the mild solution of the critical quasi-geostrophic equation
• Remark on the uniqueness of the mild solution of SQG equation
• Nonuniqueness of weak solutions to the Navier-Stokes equation
• Nonuniqueness of weak solutions to the SQG equation
• On the global regularity for the supercritical SQG equation
• A new Bernstein's Inequality and the 2D Dissipative Quasi-Geostrophic Equation
• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• On the critical dissipative quasi-geostrophic equation
• Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires

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• The Derivative Structure for a Quadratic Nonlinearity and Uniqueness for SQG
• Remark on the uniqueness of the mild solution of SQG equation
• Existence and Uniqueness of the Solution to the Anisotropic Quasi-Geostrophic Equations in the Sobolev Space