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On support and invariance theorems for a stochastic system of Burgers equtions

Nowak A., Twardowska K.

Demonstratio Mathematica

2006

Vol. 39, nr 3

691-710

We prove a support theorem for a stochastic version of the Burgers system formulated for the deterministic case by Burgers in [Bu 39]. The existence and uniqueness theorem for such a stochastic system was given by Zabczyk and Twardowska in [TZ 06]. In the proof of our support theorem we use a Wong-Zakai type theorem for such a system proved by Nowak in [No 05]. We generalize the method of Mackevicius ([Ma 85]}, [Ma 86]) and Gyongy ([Gy 89]) to prove the support theorem for our stochastic system of Burgers equations. We also use some considerations from Twardowska [Tw 97a]. In our proof of the invariance theorem we use some result of Jachimiak from [Ja 98].