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arXiv · 1506.08773

Space-time paraproducts for paracontrolled calculus, 3d-PAM and multiplicative Burgers equations

I. Bailleul·F. Bernicot·D. Frey
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Abstract

We sharpen in this work the tools of paracontrolled calculus in order to provide a complete analysis of the parabolic Anderson model equation and Burgers system with multiplicative noise, in a $3$-dimensional Riemannian setting, in either bounded or unbounded domains. With that aim in mind, we introduce a pair of intertwined space-time paraproducts on parabolic H\"older spaces, with good continuity, that happens to be pivotal and provides one of the building blocks of higher order paracontrolled calculus.

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I. Bailleul, F. Bernicot, D. Frey. 2015-06-29. Space-time paraproducts for paracontrolled calculus, 3d-PAM and multiplicative Burgers equations. https://arxiv.org/abs/1506.08773

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