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• W2073205557 abstract "We study a generalized 1d periodic SPDE of Burgers type: $$begin{aligned} partial _t u =- A^theta u + partial _x u^2 + A^{theta /2} xi end{aligned}$$ where $$theta > 1/2$$ , $$-A$$ is the 1d Laplacian, $$xi $$ is a space–time white noise and the initial condition $$u_0$$ is taken to be (space) white noise. We introduce a notion of weak solution for this equation in the stationary setting. For these solutions we point out how the noise provide a regularizing effect allowing to prove existence and suitable estimates when $$theta >1/2$$ . When $$theta >5/4$$ we obtain pathwise uniqueness. We discuss the use of the same method to study different approximations of the same equation and for a model of stationary 2d stochastic Navier–Stokes evolution." @default.
• W2073205557 created "2016-06-24" @default.
• W2073205557 creator A5002317619 @default.
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• W2073205557 date "2013-05-21" @default.
• W2073205557 modified "2023-10-02" @default.
• W2073205557 title "Regularization by noise and stochastic Burgers equations" @default.
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• W2073205557 doi "https://doi.org/10.1007/s40072-013-0011-5" @default.
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