The Surface Quasi-geostrophic Equation With Random Diffusion

  title={The Surface Quasi-geostrophic Equation With Random Diffusion},
  author={Tristan Buckmaster and Andrea R. Nahmod and Gigliola Staffilani and Klaus Widmayer},
  journal={International Mathematics Research Notices},
Consider the surface quasi-geostrophic equation with random diffusion, white in time. We show global existence and uniqueness in high probability for the associated Cauchy problem satisfying a Gevrey type bound. This article is inspired by a recent work of Glatt-Holtz and Vicol [16]. 
mSQG equations in distributional spaces and point vortex approximation
Existence of distributional solutions of a modified surface quasi-geostrophic equation is proved for $$\mu $$μ-almost every initial condition, where $$\mu $$μ is a suitable Gaussian measure. The
Global solutions of aggregation equations and other flows with random diffusion
Aggregation equations, such as the parabolic-elliptic Patlak-Keller-Segel model, are known to have an optimal threshold for global existence vs. finite-time blow-up. In particular, if the diffusion
Invariant Measures and Global Well Posedness for the SQG Equation
We construct an invariant measure $\mu$ for the Surface Quasi-Geostrophic (SQG) equation and show that almost all functions in the support of $\mu$ are initial conditions of global, unique solutions
Randomness and Nonlinear Evolution Equations
In this paper we survey some results on existence, and when possible also uniqueness, of solutions to certain evolution equations obtained by injecting randomness either on the set of initial data or
Discrete SQG models with two boundaries and baroclinic instability of jet flows
In this paper, new vertically discrete versions of the surface quasigeostrophic (SQG) model with two boundaries are formulated. For any number of partition levels, the equations of the discrete model


Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
Motivated by the critical dissipative quasi-geostrophic equation, we prove that drift-diffusion equations with L 2 initial data and minimal assumptions on the drift are locally Holder continuous. As
A Maximum Principle Applied to Quasi-Geostrophic Equations
We study the initial value problem for dissipative 2D Quasi-geostrophic equations proving local existence, global results for small initial data in the super-critical case, decay of Lp-norms and
Global Weak Solutions to the Inviscid 3D Quasi-Geostrophic Equation
In this article, the authors prove the existence of global weak solutions to the inviscid three-dimensional quasi-geostrophic equation. This equation models the evolution of the temperature on the
Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
We give an elementary proof of the global well-posedness for the critical 2D dissipative quasi-geostrophic equation. The argument is based on a non-local maximum principle involving appropriate
Global Well-Posedness in the Super-Critical Dissipative Quasi-Geostrophic Equations
Abstract: We consider the quasi-geostrophic equation with the dissipation term, κ (-Δ)α θ, In the case , Constantin-Cordoba-Wu [6] proved the global existence of strong solution in H1 and H2 under
Global Smooth Solutions for the Inviscid SQG Equation
In this paper, we show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation.
Well-posedness of the transport equation by stochastic perturbation
We consider the linear transport equation with a globally Hölder continuous and bounded vector field, with an integrability condition on the divergence. While uniqueness may fail for the
We review some results concerning the apparition of finite time singularities in nonlinear Schrödinger equations with a Gaussian additive noise which is white in time and correlated in space. We then
Existence and Regularity of Weak Solutions to the Quasi-Geostrophic Equations in the Spaces Lp or $$\dot{H}^{-1/2}$$
In this paper we study the 2D quasi-geostrophic equation with and without dissipation. We give global existence results of weak solutions for an initial data in the space Lp or $$\dot{H}^{-1/2}$$ .
Blow-up for the stochastic nonlinear Schrödinger equation with multiplicative noise
We study the influence of a multiplicative Gaussian noise, white in time and correlated in space, on the blow-up phenomenon in the supercritical nonlinear Schrodinger equation. We prove that any