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 prove the global well-posedness to the 2D Oldroyd-B type models with $\nu\Lambda^{2\alpha}u$ and $\eta\Lambda^{2\beta}\tau$ satisfying $(i)\ \alpha>1,\eta=0$ or $(ii)\ \alpha=1,\ \beta>0$. By establishing the gradient estimate of$u$, $\tau$ and $L^\infty$ bound of ${\rm curl u+\Lambda^{-2}curldiv \tau}$,Elgidi-Rousset (Commun. Pure Appl. Math. online, 2015) obtained the globalwell-posedness for the case $\nu=0$, $\beta=1$. However, for the cases $(i)$and $(ii)$, it is difficult to improve the regularity of $u$ and $\tau$directly, especially when $\alpha\rightarrow 1^{+}$ in case $(i)$ and$\beta\rightarrow 0^{+}$ in case $(ii)$. To overcome this difficulty, weexploit a new structure of the equations coming from the dissipation andcoupled term. Then we prove the global well-posedness to these cases by energymethod which brings us closer to the more interesting case $\alpha=1$,$\eta=0$.

Global well-posedness to the subcritical Oldroyd-B type models in 2D