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/

Zendy Plus

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

Zendy Tools

Zendy Open

In this paper, we consider the 1D compressible Euler equation with thedamping coefficient $\lambda/(1+t)^{\mu}$. Under the assumption that $0\leq \mu<1$ and $\lambda >0$ or $\mu=1$ and $\lambda > 2$, we prove that solutionsexist globally in time, if initial data are small $C^1$ perturbation nearconstant states. In particular, we remove the conditions on the limit$\lim_{|x| \rightarrow \infty} (u (0,x), v (0,x))$, assumed in previousresults.

Remark on global existence of solutions to the 1D compressible Euler equation with time-dependent damping