Probabilistic well-posedness for the cubic wave equation

Burq, Nicolas, and Tzvetkov, Nikolay. "Probabilistic well-posedness for the cubic wave equation." Journal of the European Mathematical Society 016.1 (2014): 1-30. <http://eudml.org/doc/277732>.

@article{Burq2014,
abstract = {The purpose of this article is to introduce for dispersive partial differential equations with random initial data, the notion of well-posedness (in the Hadamard-probabilistic sense). We restrict the study to one of the simplest examples of such equations: the periodic cubic semi-linear wave equation. Our contributions in this work are twofold: first we break the algebraic rigidity involved in our previous works and allow much more general randomizations (general infinite product measures v.s. Gibbs measures), and second, we show that the flow that we are able to construct enjoys very nice dynamical properties, including a new notion of probabilistic continuity.},
author = {Burq, Nicolas, Tzvetkov, Nikolay},
journal = {Journal of the European Mathematical Society},
keywords = {random series; wave equations; well-posedness; cubic wave equation; probabilistic well-posedness; random Fourier series; cubic wave equation; probabilistic well-posedness; random Fourier series},
language = {eng},
number = {1},
pages = {1-30},
publisher = {European Mathematical Society Publishing House},
title = {Probabilistic well-posedness for the cubic wave equation},
url = {http://eudml.org/doc/277732},
volume = {016},
year = {2014},
}

TY - JOUR
AU - Burq, Nicolas
AU - Tzvetkov, Nikolay
TI - Probabilistic well-posedness for the cubic wave equation
JO - Journal of the European Mathematical Society
PY - 2014
PB - European Mathematical Society Publishing House
VL - 016
IS - 1
SP - 1
EP - 30
AB - The purpose of this article is to introduce for dispersive partial differential equations with random initial data, the notion of well-posedness (in the Hadamard-probabilistic sense). We restrict the study to one of the simplest examples of such equations: the periodic cubic semi-linear wave equation. Our contributions in this work are twofold: first we break the algebraic rigidity involved in our previous works and allow much more general randomizations (general infinite product measures v.s. Gibbs measures), and second, we show that the flow that we are able to construct enjoys very nice dynamical properties, including a new notion of probabilistic continuity.
LA - eng
KW - random series; wave equations; well-posedness; cubic wave equation; probabilistic well-posedness; random Fourier series; cubic wave equation; probabilistic well-posedness; random Fourier series
UR - http://eudml.org/doc/277732
ER -