Stochastic Euler equations on the torus. (English) Zbl 0952.35164

A two-dimensional stochastic Euler equation \[ \roman du = -\langle u,\nabla\rangle \roman dt + f(t,u) \roman dt + g(t,u) \roman dw, \quad \text{div} u = 0, \tag{1} \] with the periodic boundary condition is considered. Let \(L>0\), let \(H\) be the closure of the set \(\{u|_{[0,L]^2}; u\in C^\infty(\mathbb{R}^2;\mathbb{R}^2), \text{}u\) \(L\)-periodic


35R60 PDEs with randomness, stochastic partial differential equations
35Q05 Euler-Poisson-Darboux equations
26E35 Nonstandard analysis
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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