5 papers · 1 filter
On probabilistic ill-posedness
Tadahiro Oh, Nikolay Tzvetkov
In this note, we introduce an enhanced notion of probabilistic well-posedness for dispersive PDEs with random initial data by imposing stability at the origin as the amplitude of r…
Hyperbolic -model on the plane
Tadahiro Oh, Leonardo Tolomeo, Yuzhao Wang +1
We study the hyperbolic -model on the plane. By establishing coming down from infinity for the associated stochastic nonlinear heat equation (SNLH) on the plane, we fir…
On the deep-water and shallow-water limits of the intermediate long wave equation from a statistical viewpoint
Guopeng Li, Tadahiro Oh, Guangqu Zheng
(Due to the limit on the number of characters for an abstract set by arXiv, the full abstract can not be displayed here. See the abstract in the paper.) We study convergence proble…
Norm inflation for the cubic nonlinear heat equation above the scaling critical regularity
Ilya Chevyrev, Tadahiro Oh, Yuzhao Wang
We consider the ill-posedness issue for the cubic nonlinear heat equation and prove norm inflation with infinite loss of regularity in the Hölder-Besov space $\mathcal C^s = B^{s}…
A remark on randomization of a general function of negative regularity
Tadahiro Oh, Mamoru Okamoto, Oana Pocovnicu +1
In the study of partial differential equations (PDEs) with random initial data and singular stochastic PDEs with random forcing, we typically decompose a classically ill-defined so…