In this paper we establish the large deviation principle for the the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity both for small noise and for short time.The proof for large deviation ...In this paper we establish the large deviation principle for the the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity both for small noise and for short time.The proof for large deviation principle is based on the weak convergence approach.For small time asymptotics we use the exponential equivalence to prove the result.展开更多
This work aims to prove the large deviation principle for a class of stochastic partial differential equations with locally monotone coefficients under the extended variational framework, which generalizes many previo...This work aims to prove the large deviation principle for a class of stochastic partial differential equations with locally monotone coefficients under the extended variational framework, which generalizes many previous works. Using stochastic control and the weak convergence approach, we prove the Laplace principle,which is equivalent to the large deviation principle in our framework. Instead of assuming compactness of the embedding in the corresponding Gelfand triple or finite dimensional approximation of the diffusion coefficient in some existing works, we only assume some temporal regularity in the diffusion coefficient.展开更多
基金Research supported in part by NSFC(No.11771037)Key Lab of Random Complex Structures and Data Science,Chinese Academy of ScienceFinancial the DFG through the CRC 1283“Taming uncertainty and profiting from randomness and low regularity in analysis,stochastics and their applications”。
文摘In this paper we establish the large deviation principle for the the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity both for small noise and for short time.The proof for large deviation principle is based on the weak convergence approach.For small time asymptotics we use the exponential equivalence to prove the result.
基金National Natural Science Foundation of China (Grant Nos. 11501147, 11501509, 11822106 and 11831014)the Natural Science Foundation of Jiangsu Province (Grant No. BK20160004)the Qing Lan Project and the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘This work aims to prove the large deviation principle for a class of stochastic partial differential equations with locally monotone coefficients under the extended variational framework, which generalizes many previous works. Using stochastic control and the weak convergence approach, we prove the Laplace principle,which is equivalent to the large deviation principle in our framework. Instead of assuming compactness of the embedding in the corresponding Gelfand triple or finite dimensional approximation of the diffusion coefficient in some existing works, we only assume some temporal regularity in the diffusion coefficient.
