Surface Waves for a Compressible Viscous Fluid
Surface Waves for a Compressible Viscous Fluid
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可压缩粘性流体的表面波
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
A. Tani
中科院分区：
文献类型：
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作者：
N. Tanaka;A. Tani
摘要在这篇文章中，我们考虑的是自由边界问题。
可压缩粘性各向同性牛顿流体。
我们的问题是找到由
固定底部以下和固定底部以上的液体
由自由面与密度、速度
矢量场与流体的绝对温度
满足Navier-Stokes方程组和
初始边界条件。
Navier-Stokes方程由以下守恒量组成
质量、动量在向下的引力场作用下
方向和能量。
考虑了表面张力对自由表面的影响
考虑到了。
本文的目的是建立两个存在定理。
对于上面提到的问题：第一个涉及
各向异性中的临时局部可解性
Soblev-Slobodeskiĭ空间和第二类整体
平衡静止态附近的可解性。
这里的平衡静止态(导热状态)是指
温度分布是线性函数，与
相对于垂直方向，密度由下式确定
一个常微分方程式，其中包含
州政府。为了证明，我们依赖于Solonnikov在
不可压缩流体的情况，经过一些修改，因为我们的
问题是双曲-抛物线耦合系统。
AbstractIn this paper, we are concerned with free boundary problem for
compressible viscous isotropic Newtonian fluid.
Our problem is to find the three-dimensional domain occupied by
the fluid which is bounded below by the fixed bottom and above
by the free surface together with the density, the velocity
vector field and the absolute temperature of the fluid
satisfying the system of Navier-Stokes equations and the
initial-boundary conditions.
The Navier-Stokes equations consist of the conservations of
mass, momentum under the gravitational field in a downward
direction and energy.
The effect of the surface tension on the free surface is taken
into account.
The purpose of this paper is to establish two existence theorems
to the problem mentioned above: the first concerns with the
temporary local solvability in anisotropic
Sobolev-Slobodetskiĭ spaces and the second the global
solvability near the equilibrium rest state.
Here the equilibrium rest state (heat conductive state) means
that the temperature distribution is a linear function with
respect to a vertical direction and the density is determined by
an ordinary differential equation which involves equation of
state. For the proof, we rely on the methods due to Solonnikov in the
case of incompressible fluid with some modifications, since our
problem is hyperbolic-parabolic coupled system.