相关论文: Existence of Non-Decaying Solutions to the General…

We establish short-time existence of solutions to the surface quasi-geostrophic equation in both the H\"{o}lder spaces $C^r(\mathbb{R}^2)$ for $r>1$ and the uniformly local Sobolev spaces $H^s_{ul}(\mathbb{R}^2)$ for $s\geq 3$. Using…

In this paper, we focus on the two-dimensional surface quasi-geostrophic equation with fractional horizontal dissipation and vertical thermal diffusion which represents a general case of the classical surface quasi-geostrophic equation. On…

In \cite{YZ}, the author proved the global existence of the two-dimensional anisotropic quasi-geostrophic equations with condition on the parameters $\alpha,$ $\beta$ in the Sobolev spaces $H^s( \R^2)$; $s\geq 2$. In this paper, we show…

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…

In this paper, we show that the global solution of the surface anisotropic two-dimensional quasi-geostrophic equation with fractional horizontal dissipation and vertical thermal diffusion established by the author in [2] is bounded in…

We develop a theory of self-similar solutions to the critical surface quasi-geostrophic equations. We construct self-similar solutions for arbitrarily large data in various regularity classes and demonstrate, in the small data regime,…

We consider the surface quasi-geostrophic equation in two spatial dimensions, with subcritical diffusion (i.e. with fractional diffusion of order $2\alpha$ for $\alpha>\frac{1}{2}$.) We establish existence of solutions without assuming…

This paper studies the dissipative generalized surface quasi-geostrophic equations in a supercritical regime where the order of the dissipation is small relative to order of the velocity, and the velocities are less regular than the…

In the present study, we find that the surface quasi-geostrophic equation admits exact solutions, which evolve with time in quasi-stationary states. The solutions presented are available for any dissipation effect $\kappa (-\Delta)^\alpha$…

Motivated by the recent work of Hassainia and Hmidi [Z. Hassainia, T. Hmidi - On the {V}-states for the generalized quasi-geostrophic equations,arXiv preprint arXiv:1405.0858], we close the question of the existence of convex global…

We consider classical solutions of the inviscid Surface Quasi-geostrophic equation that are a small perturbation $\epsilon$ from a radial stationary solution $\theta=|x|$. We use a modified energy method to prove the existence time of…

In this article, we study the critical dissipative surface quasi-geostrophic equation (SQG) in $ \mathbb{R}^2$. Motivated by the study of the homogeneous statistical solutions of this equation, we show that for any large initial data…

In this paper, we study the super-critical Quasi-Geostrophic equation in Gevrey-Sobolev space. We prove the local existence of $(QG)$ for any large initial data and we give an exponential type of Blow-up to the solution. Moreover, we…

In this paper, we consider the model of 3D incompressible Navier-Stokes equations and 2D supercritical Surface Quasi-Geostrophic equations with time oscillation in the nonlinear term. We obtain that there exists global smooth solution of…

We consider a nonlinear, spatially-nonlocal initial value problem in one space dimension on $\mathbb{R}$ that describes the motion of surface quasi-geostrophic (SQG) fronts. We prove that the initial value problem has a unique local smooth…

In this paper, we study the existence of global classical solutions to the generalized surface quasi-geostrophic equation. By using the variational method, we provide some new families of global classical solutions for to the generalized…

We show the existence of nontrivial stationary weak solutions to the surface quasi-geostrophic equations on the two dimensional periodic torus.

We study the critical dissipative quasi-geostrophic equations in $\bR^2$ with arbitrary $H^1$ initial data. After showing certain decay estimate, a global well-posedness result is proved by adapting the method in [11] with a suitable…

In this paper we construct a large class of non-trivial (non-radial) self-similar solutions of the generalized surface quasi-geostrophic equation (gSQG). To the best of our knowledge, this is the first rigorous construction of any…

We establish the global existence of higher-order Sobolev solutions for a non-local integrable evolution equation arising in the study of pseudospherical surfaces and non-linear wave propagation. Under a natural assumption on the initial…