论文标题
额定圆柱体中不可压缩的粘性流体的本地良好性，$ 90^\ circ $ -contact角度
Local well-posedness of incompressible viscous fluids in bounded cylinders with $90^\circ$-contact angle
论文作者
论文摘要
我们考虑了Navier的自由边界问题 - 带有移动接触线的三维欧几里得空间中的Stokes方程，其中构成了90 $^\ Circ $ - 接触角条件。我们证明，对于给定的$ t> 0 $，如果初始数据很小，则问题是$（0，t）$上的本地供应良好。与Wilke（2013）中的策略相反，我们研究了$ l^p $的转换问题，并在空间设置中$ l^q $ -in-in-in-In-In-In-Ink $ l^q $ -in。
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.
