Small time asymptotics for SPDEs with locally monotone coefficients. (English) Zbl 1464.60066
Summary: 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.
MSC:
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 60F10 | Large deviations |
| 76S05 | Flows in porous media; filtration; seepage |
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
| 35K57 | Reaction-diffusion equations |
Keywords:
small time asymptotics; large deviation principle; stochastic partial differential equations; locally monotone; porous medium equationReferences:
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