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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

MSC:

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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References:

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[2] Capi ński, M. and Cutland, N. J. (1995). Nonstandard Methods for Stochastic Fluid Mechanics. World Scientific, Singapore. · Zbl 0824.76003
[3] Hurd, A. E. and Loeb, P. A. (1985). An Introduction to Nonstandard Real Analy sis. Academic Press, New York. · Zbl 0583.26006
[4] Temam, R. (1983). Navier-Stokes Equations and Nonlinear Functional Analy sis. SIAM, Philadelphia. · Zbl 0522.35002
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