相关论文: On the global regularity for the supercritical SQG…

We consider the SQG equation with dissipation given by a fractional Laplacian of order $\alpha<\frac{1}{2}$. We introduce a notion of suitable weak solution, which exists for every $L^2$ initial datum, and we prove that for such solution…

In this paper, we prove the global regularity of smooth solutions to 2D surface quasi-geostrophic (SQG) equations with super-critical dissipation for a class of large initial data, where the velocity and temperature can be arbitrarily large…

In this paper, we consider the following anisotropic quasi-geostrophic equations \begin{equation}\tag*{$(AQG)_{\alpha,\beta}$} \partial_t\theta+ u_\theta.\nabla\theta +\mu|\partial_1|^{2\alpha}\theta+\nu |\partial_2|^{2\beta}\theta=0,\quad…

We study the critical and super-critical dissipative quasi-geostrophic equations in $\bR^2$ or $\bT^2$. Higher regularity of mild solutions with arbitrary initial data in $H^{2-\gamma}$ is proved. As a corollary, we obtain a global…

This paper is devoted to the global (in time) regularity problem for a family of active scalar equations with fractional dissipation. Each component of the velocity field $u$ is determined by the active scalar $\theta$ through $\mathcal{R}…

We study the long time behavior of regular solutions of the supercritical gSQG equations in the fully nonlinear regime. More precisely, under the assumption of small initial data in the critical Sobolev norm, we prove the existence of the…

In this paper, we prove that if the initial data $\theta_0$ and its Riesz transforms ($\mathcal{R}_1(\theta_0)$ and $\mathcal{R}_2(\theta_0)$) belong to the space $(\overline{S(\mathbb{R}^2))}^{B_{\infty}^{1-2\alpha ,\infty}}$, where…

We consider the 2D quasi-geostrophic equation with supercritical dissipation and dispersive forcing in the whole space. When the dispersive amplitude parameter is large enough, we prove the global well-posedness of strong solution to the…

This paper aims at the global regularity problem concerning the 2D incompressible Boussinesq equations with general critical dissipation. The critical dissipation refers to $\alpha +\beta=1$ when $\Lambda^\alpha \equiv…

We consider the dissipative generalized Surface Quasi-Geostrophic equation with dissipation given by any fractional power of the Laplacian. In the inviscid limit, it is proved that anomalous dissipation of the Hamiltonian is prevented by…

We examine the regularity of weak solutions of quasi-geostrophic (QG) type equations with supercritical ($\alpha <1/2$) dissipation $(-\Delta)^\alpha$. This study is motivated by a recent work of Caffarelli and Vasseur, in which they study…

In this paper we show the global existence for critical dissipative quasi-geostrophic equations if $\|\widehat{\theta^0}\|_{L^1}$ is small enough; among others we prove the analyticity of such a solution. If in addition the initial…

We consider surface quasi-geostrophic equation with dispersive forcing and critical dissipation. We prove global existence of smooth solutions given sufficiently smooth initial data. This is done using a maximum principle for the solutions…

We consider a family of singular surface quasi-geostrophic equations $$ \partial_{t}\theta+u\cdot\nabla\theta=-\nu (-\Delta)^{\gamma/2}\theta+(-\Delta)^{\alpha/2}\xi,\qquad u=\nabla^{\perp}(-\Delta)^{-1/2}\theta, $$ on…

The present article is devoted to the 3D dissipative quasi-geostrophic system (QG). This system can be obtained as limit model of the Primitive Equations in the asymptotics of strong rotation and stratification, and involves a non-radial,…

We present a regularity result for weak solutions of the 2D quasi-geostrophic equation with supercritical ($\alpha< 1/2$) dissipation $(-\Delta)^\alpha$ : If a Leray-Hopf weak solution is H\"{o}lder continuous $\theta\in C^\delta({\mathbb…

This is a remark that by using an adaptation of the technique invented by A. Kiselev, F. Nazarov, and A. Voldberg, with a modified scaling argument, we can prove global regularity of the critical 2-D dissipative quasi-geostrophic equation…

The initial value problem for the two dimensional dissipative quasi-geostrophic equation derived from geophisical fluid dynamics is studied. The dissipation of this equation is given by the fractional Laplacian. It is known that the half…

We consider the initial value problem for a pseudodifferential equation with first order hyperbolic part, and an order $\gamma > 0$ dissipative term. Under an assumption, depending on an integer parameter $L \geq 2$ such that $2 \gamma <…

We study the global well-posedness of the supercritical dissipative surface quasi-geostrophic (SQG) equation, a key model in geophysical fluid dynamics. While local well-posedness is known, achieving global well-posedness for large initial…