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

The surface growth model, $u_t + u_{xxxx} + \partial_{xx} u_x^2 =0$, is aone-dimensional fourth order equation, which shares a number of strikingsimilarities with the three-dimensional incompressible Navier--Stokesequations, including the results regarding existence and uniqueness ofsolutions and the partial regularity theory. Here we show that a weak solutionof this equation is smooth on a space-time cylinder $Q$ if the Serrin condition$u_x\in L^{q'}L^q (Q)$ is satisfied, where $q,q'\in [1,\infty ]$ are such thateither $1/q+4/q'<1$ or $1/q+4/q'=1$, $q'<\infty$.

A sufficient integral condition for local regularity of solutions to the surface growth model