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

We use the Cole--Hopf transformation and the Laplace method for the heatequation to justify the numerical results on enstrophy growth in the viscousBurgers equation on the unit circle. We show that the maximum enstrophyachieved in the time evolution is scaled as $\mathcal{E}^{3/2}$, where$\mathcal{E}$ is the large initial enstrophy, whereas the time needed forreaching the maximal enstrophy is scaled as $\mathcal{E}^{-1/2}$. These boundsare sharp for sufficiently smooth initial conditions.

Sharp bounds on enstrophy growth in the viscous Burgers equation