# The Surface Quasi-geostrophic Equation With Random Diffusion

@article{Buckmaster2018TheSQ,
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},
year={2018}
}
• Published 10 June 2018
• Mathematics
• 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].
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## References

SHOWING 1-10 OF 31 REFERENCES
Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• Physics, Mathematics
• 2006
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
• Mathematics
• 2004
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
• Environmental Science, Mathematics
• 2014
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
• Mathematics
• 2007
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
• Mathematics
• 2003
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
• Mathematics
• 2016
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
• Mathematics
• 2008
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
FINITE-TIME BLOW-UP IN THE ADDITIVE SUPERCRITICAL STOCHASTIC NONLINEAR SCHRÖDINGER EQUATION : THE REAL NOISE CASE
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
• Mathematics
• 2005
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