LOCAL AND GLOBAL EXISTENCE OF SMOOTH SOLUTIONS FOR THE STOCHASTIC EULER EQUATIONS WITH MULTIPLICATIVE NOISE

We establish the local existence of pathwise solutions for the stochastic Euler equations in a three-dimensional bounded domain with slip boundary conditions and a suitable nonlinear multiplicative noise. In the two-dimensional case we obtain the global existence of these solutions with additive or...

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Veröffentlicht in:	The Annals of probability 2014-01, Vol.42 (1), p.80-145
Hauptverfasser:	Glatt-Holtz, Nathan E., Vicol, Vlad C.
Format:	Artikel
Sprache:	eng
Schlagworte:	35Q35 60H15 76B03 A priori knowledge Boundary conditions Brownian motion compactness methods Determinism Euler equations Eulers equations Martingales Mathematical problems Navier Stokes equation Noise nonlinear multiplicative noise Partial differential equations pathwise solutions Probability Signal processing Stochastic models stochastic partial differential equations on Lebesgue spaces Stopping distances Studies Uniqueness
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