Almost sure local well-posedness at regularities as low as S > (2 - sigma)/4 is proved for a class of cubic dispersive PDEs with Wiener randomized initial data, using higher-order expansions and sector-adapted directional norms.
Three-dimensional dispersion of nonlinear ity and sta- bility of multidimensional solitons
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Probabilistic well-posedness of generalized cubic nonlinear Schr\"odinger equations with strong dispersion using higher order expansions
Almost sure local well-posedness at regularities as low as S > (2 - sigma)/4 is proved for a class of cubic dispersive PDEs with Wiener randomized initial data, using higher-order expansions and sector-adapted directional norms.