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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this article, we prove that the equation  \begin{equation*}  \left\{\begin{split}  &(\partial^2_t-\Delta)u+|u|^{p-1}u=0,\ \ \ 3\leq p<5  &\big(u(0),\partial_tu(0)\big)=(u_0,u_1)\in H^{s}(\mathbb{T}^3)\timesH^{s-1}(\mathbb{T}^3)=:\mathcal{H}^s(\mathbb{T}^3)  \end{split}\right.  \end{equation*} with $s<\frac{3}{2}-\frac{2}{p-1}$ is everywhere ill-posed.This work also indicates that, only properly regularizing the initial data canwe smoothly approximate the solutions constructed in \cite{BT14} and\cite{Xia14}.

Generic ill-posedness for wave equation of power type on 3D torus