大偏差原理与无粘壳模型
Large deviation principle and inviscid shell models
摘要：
证明了无粘壳湍流模型的一个LDP。当粘性系数收敛到0且噪声强度乘以粘性的平方根时，我们证明了某些具有由H值布朗运动驱动的乘性随机扰动的湍流壳模型在[0，T]上的一致收敛一致收敛拓扑下满足C（[0，T]，V）中的LDP，但其中V被赋予比自然拓扑弱的拓扑.初始条件必须属于V和证明是基于一个家庭的随机控制方程的弱收敛。速率函数描述的无粘方程的解决方案。
英文摘要：
A LDP is proved for the inviscid shell model of turbulence. As the viscosity coefficient converges to 0 and the noise intensity is multiplied by the square root of the viscosity, we prove that some shell models of turbulence with a multiplicative stochastic perturbation driven by a H-valued Brownian motion satisfy a LDP in C([0,T],V) for the topology of uniform convergence on [0,T], but where V is endowed with a topology weaker than the natural one. The initial condition has to belong to V and the proof is based on the weak convergence of a family of stochastic control equations. The rate function is described in terms of the solution to the inviscid equation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
