Projects per year
Abstract
We study the threedimensional cubic nonlinear wave equation (NLW) with random initial data below L^2(T^3). By considering the second order expansion in terms of the random linear solution, we prove almost sure local wellposedness of the renormalized NLW in negative Sobolev spaces. We also prove a new instability result for the defocusing cubic NLW without renormalization in negative Sobolev spaces, which is in the spirit of the socalled triviality in the study of stochastic partial differential equations. More precisely, by studying (unrenormalized) NLW with
given smooth deterministic initial data plus a certain truncated random initial data,
we show that, as the truncation is removed, the solutions converge to 0 in the distributional sense for any deterministic initial data.
given smooth deterministic initial data plus a certain truncated random initial data,
we show that, as the truncation is removed, the solutions converge to 0 in the distributional sense for any deterministic initial data.
Original language  English 

Number of pages  43 
Journal  Annales de l'Institut Fourier 
Publication status  Accepted/In press  28 Oct 2020 
Fingerprint
Dive into the research topics of 'Probabilistic local wellposedness of the cubic nonlinear wave equation in negative Sobolev spaces'. Together they form a unique fingerprint.Projects
 1 Finished

ProbDynDispEq  Probabilistic and Dynamical Study of Nonlinear Dispersive Equations
1/03/15 → 29/02/20
Project: Research