Global infinite energy solutions for the cubic wave equation
Nicolas Burq (LM-Orsay), Laurent Thomann (LMJL), Nikolay Tzvetkov, (AGM)
TL;DR
This paper demonstrates the existence of global solutions with infinite energy for the cubic wave equation in higher dimensions, using probabilistic methods to handle typical initial data.
Contribution
It establishes the existence of infinite energy solutions in dimensions greater than 3 for the cubic wave equation via probabilistic techniques.
Findings
Existence of infinite energy solutions in dimensions > 3
Solutions are typical with respect to certain probability measures
Advances understanding of wave equations with infinite energy data
Abstract
We prove the existence of infinite energy global solutions of the cubic wave equation in dimension greater than 3. The data is a typical element on the support of suitable probability measures.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Stability and Controllability of Differential Equations · Navier-Stokes equation solutions