相关论文: mSQG equations in distributional spaces and point …
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…
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…
Stationary solutions to a Fokker-Planck equation corresponding to a noisy logistic equation with correlated Gaussian white noises are constructed. Stationary distributions exist even if the corresponding deterministic system displays an…
We are concerned with the existence of periodic travelling-wave solutions for the generalized surface quasi-geostrophic (gSQG) equation(including incompressible Euler equation), known as von K\'arm\'an vortex street. These solutions are of…
We consider homogeneous (stationary self-similar) solutions to the generalized surface quasi-geostrophic (gSQG) equations parametrized by the constant $0<s<1$, representing the 2D Euler equations ($s=1$), the SQG equations $(s=1/2)$, and…
This monograph addresses an important problem in mathematical fluid dynamics: constructing stable, long-term solutions to certain quasilinear evolution equations. We implement an elaborate scheme for building global quasiperiodic solutions…
We study stochastic SQG equations on the torus $\mathbb{T}^2$ with multiplicative transport noise in the $L^2$-setting. Under a suitable scaling of the noise, we show that the solutions converge weakly to the unique solution to the…
In this paper, we present a new and elementary proof of the local existence and uniqueness of the classical solution to the Cauchy problem of the two-dimensional generalized surface quasi-geostrophic (SQG) equation via the method of the…
We prove the global regularity of smooth solutions for a dissipative surface quasi-geostrophic equation with both velocity and dissipation logarithmically supercritical compared to the critical equation. By this, we mean that a symbol…
Point vortex models are presented for the generalized Euler equations, which are characterized by a fractional Laplacian relation between the active scalar and the streamfunction. Special focus is given to the case of the surface…
A stochastic version of the two-layer quasi-geostrophic model (2LQG) with multiplicative transport noise is analysed. This popular intermediate complexity model describes large scale atmosphere and ocean dynamics at the mid-latitudes. The…
We consider the well-posedness of the surface quasi-geostrophic (SQG) front equation. Hunter-Shu-Zhang [9] established well-posedness under a small data condition as well as a convergence condition on an expansion of the equation's…
We study the scattering behavior of global solutions to stochastic nonlinear Schr\"odinger equations with linear multiplicative noise. In the case where the quadratic variation of the noise is globally finite and the nonlinearity is…
We propose a novel algorithm for the approximation of surface-quasi geostrophic (SQG) flows modeled by a nonlinear partial differential equation coupling transport and fractional diffusion phenomena. The time discretization consists of an…
We use a nonlocal maximum principle to prove the global existence of smooth solutions for a slightly supercritical surface quasi-geostrophic equation. By this we mean that the velocity field $u$ is obtained from the active scalar $\theta$…
The quasigeostrophic model is a simplified geophysical fluid model at asymptotically high rotation rate or at small Rossby number. We consider the quasigeostrophic equation with dissipation under random forcing in bounded domains. We show…
In this article, we consider the stochastic wave equation in spatial dimension $d=1$, with linear term $\sigma(u)=u$ multiplying the noise. This equation is driven by a Gaussian noise which is white in time and fractional in space with…
We consider the asymptotic behavior of the surface quasi-geostrophic equation, subject to a small external force. Under suitable assumptions on the forcing, we first construct the steady states and we provide a number of useful a posteriori…
We prove local well-posedness in the Sobolev spaces $\dot H^s(\mathbb{T})$, with $s>7/2$, for an initial value problem for a nonlocal, cubically nonlinear, dispersive equation that provides an approximate description of the evolution of…
We construct examples of solutions to the conservative surface quasi-geostrophic (SQG) equation that must either exhibit infinite in time growth of derivatives or blow up in finite time.