具有$90^\circ$ -接触角的有界圆柱中不可压缩粘性流体的局部适定性
Local well-posedness of incompressible viscous fluids in bounded cylinders with $90^\circ$-contact angle
摘要：
考虑三维欧几里得空间中斯托克斯方程的一个具有移动接触线的自由边界问题，其中提出了90 ° $^\circ$接触角条件.我们表明，对于给定的$T > 0$的问题是局部适定的$(0, T)$提供的初始数据是小的。与Wilke（2013）中的策略相反，我们在$L^p$ -in-time和$L^q$ -in-space设置中研究了转换问题，这产生了初始数据的最佳正则性。
英文摘要：
We consider a free boundary problem of the Navier--Stokes equations in the three-dimensional Euclidean space with moving contact line, where the 90$^\circ$-contact angle condition is posed. We show that for given $T > 0$ the problem is local well-posed on $(0, T)$ provided that the initial data are small. In contrast to the strategy in Wilke (2013), we study the transformed problem in an $L^p$-in-time and $L^q$-in-space setting, which yields the optimal regularity of the initial data.
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