arXiv subjects

Taiki Okazaki

Publications and source records attributed to Taiki Okazaki.

3 recordsLinked to original sources

arXiv2026

Uniqueness of the dissipative SQG without time-continuity assumption

We consider the uniqueness of the solution of the dissipative surface quasi-geostrophic equation, without assuming time-continuity and smallness of the solutions. We show that the uniqueness holds in the scale-critical Lebesgue spaces and non-homogeneous Besov spaces. The proof is based on the energy method, inspired by the approach introduced by Lions and Masmoudi (2001) in the study of uniqueness for the Navier-Stokes equations. A key ingredient of the argument is the justification of the energy inequality via the smoothing effect of the fractional heat semigroup together with an iteration scheme based on the structure of the integral equation.

math.AP↗

arXiv2025

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

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.

math.AP↗

arXiv2024

On the uniqueness of the mild solution of the critical quasi-geostrophic equation

We demonstrate that the uniqueness of the mild solution of the two-dimensional quasi-geostrophic equation with the critical dissipation holds in the scaling critical homogeneous Besov space $\dot{B}^0_{\infty,1}$. We consider a solustion of integral equation, and our result does not need regularity assumption.

math.AP↗