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Small time asymptotics for SPDEs with locally monotone coefficients

  • * Corresponding author: Wei Liu

    * Corresponding author: Wei Liu 

The research of W. Liu is supported by NSFC (No. 11822106, 11831014, 11571147), the research of Y. Xie is supported by NSFC (No. 11771187, 11931004) and PAPD of Jiangsu Higher Education Institutions

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  • This work aims to prove the small time large deviation principle (LDP) for a class of stochastic partial differential equations (SPDEs) with locally monotone coefficients in generalized variational framework. The main result could be applied to demonstrate the small time LDP for various quasilinear and semilinear SPDEs such as stochastic porous medium equations, stochastic $ p $-Laplace equations, stochastic Burgers type equation, stochastic 2D Navier-Stokes equation, stochastic power law fluid equation and stochastic Ladyzhenskaya model. In particular, our small time LDP result seems to be new in the case of general quasilinear SPDEs with multiplicative noise.

    Mathematics Subject Classification: Primary: 60H15, 60F10; Secondary: 76S05, 35J92, 35K57.


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