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Small time asymptotics for a class of stochastic partial differential equations with fully monotone coefficients forced by multiplicative Gaussian noise

Ankit KumarManil T. Mohan
Dec 2022
摘要
The main goal of this article is to study the effect of small, highlynonlinear, unbounded drifts (small time large deviation principle (LDP) basedon exponential equivalence arguments) for a class of stochastic partialdifferential equations (SPDEs) with fully monotone coefficients driven bymultiplicative Gaussian noise. The small time LDP obtained in this paper isapplicable for various quasi-linear and semilinear SPDEs such as porous mediumequations, Cahn-Hilliard equation, 2D Navier-Stokes equations,convection-diffusion equation, 2D liquid crystal model, power law fluids,Ladyzhenskaya model, $p$-Laplacian equations, etc., perturbed by multiplicativeGaussian noise.
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