English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study the three-dimensional cubic nonlinear wave equation (NLW) withrandom initial data below $L^2(\mathbb{T}^3)$. By considering the second orderexpansion in terms of the random linear solution, we prove almost sure localwell-posedness of the renormalized NLW in negative Sobolev spaces. We alsoprove a new instability result for the defocusing cubic NLW withoutrenormalization in negative Sobolev spaces, which is in the spirit of theso-called triviality in the study of stochastic partial differential equations.More precisely, by studying (un-renormalized) NLW with given smoothdeterministic initial data plus a certain truncated random initial data, weshow that, as the truncation is removed, the solutions converge to $0$ in thedistributional sense for any deterministic initial data.

Probabilistic local well-posedness of the cubic nonlinear wave equation in negative Sobolev spaces