Free boundary problem of steady incompressible flow with contact angle π 2
Free boundary problem of steady incompressible flow with contact angle π 2
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接触角π 2 稳态不可压缩流自由边界问题
DOI：
10.1016/j.jde.2005.06.014
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发表时间：
2005
影响因子：
2.4
通讯作者：
B. Jin
中科院分区：
文献类型：
--
作者：
B. Jin
考虑具有自由上表面的三维容器中的流体，该容器满足平稳Navier-Stokes方程。所述容器具有光滑的壁，自由的上表面为光滑平面区域Σ的图形。从物理角度看，流体在容器壁上满足狄利克雷边界条件。另一方面，流体满足自由上表面上的混合边界条件，该条件由自由上表面上的力平衡表述。当流体在容器内流动时，由于边界条件的不同，接触线上可能产生奇点。我们证明了在Sobolev空间Wq3-1/q（Σ）， 3<q<∞，速度u∈Wq2（Ω）中，当接触角为π/2，外力为Lq（R3）中具有规则的重力小摄动时，流动填充具有规则自由曲面的域Ω的存在性。我们的解是流体静止状态的一个小扰动。
We consider a fluid in a three-dimensional container with free upper surface, which satisfies stationary Navier–Stokes equations. The container has a smooth wall and the free upper surface is a graph of smooth plane region Σ. From the physical point of view, the fluid satisfies Dirichlet boundary condition on the wall of the container. On the other hand, the fluid satisfies a mixed boundary condition on the free upper surface, which is formulated by the balances of forces on the free upper surfaces. When a fluid is flowing in the container, singularity may be developed along the contact line because of different boundary conditions. We show the existence of flow filling a domain Ω with regular free surface in a Sobolev space Wq3-1/q(Σ), 3<q<∞ and regular velocity u∈Wq2(Ω), when the contact angle is π/2 and the external force is a small perturbation of gravity with regularity in Lq(R3). Our solution is a small perturbation of a rest state of fluid.