5 papers
Radial models in supercritical regimes
Tadahiro Oh, Leonardo Tolomeo, Nikolay Tzvetkov +1
We consider the measure under radial symmetry on the unit ball, formally given by $$dρ(u) = \frac 1 Z \exp\Big( - \frac 14 \int_{B_1} |u|^4 dx - \frac 12 \int_{B_1} |\nabla…
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…
Numerical study of probabilistic well-posedness of one dimensional fractional nonlinear wave equations
Wandrille Ruffenach, Nikolay Tzvetkov
The three dimensional cubic defocusing nonlinear wave equation is known to be ill-posed for general low regularity initial data. Well-posedness can however be recovered globally in…
Probabilistic well-posedness of dispersive PDEs beyond variance blowup I: Benjamin-Bona-Mahony equation
Guopeng Li, Jiawei Li, Tadahiro Oh +1
We investigate a possible extension of probabilistic well-posedness theory of nonlinear dispersive PDEs with random initial data beyond variance blowup. As a model equation, we stu…
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…