# Probabilistic well-posedness for the cubic wave equation

Nicolas Burq; Nikolay Tzvetkov

Journal of the European Mathematical Society (2014)

- Volume: 016, Issue: 1, page 1-30
- ISSN: 1435-9855

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topBurq, 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 -

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