Evolution of compressible and incompressible fluids separated by a closed interface
Evolution of compressible and incompressible fluids separated by a closed interface
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由封闭界面分隔的可压缩和不可压缩流体的演化
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
I. Denisova
中科院分区：
文献类型：
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作者：
I. Denisova
这项工作解决了控制两种不同类型的粘性液体（可压缩和不可压缩）同时运动的问题。流体之间的边界被视为未知（自由）界面，其中考虑了表面张力。尽管流体占据了整个空间 R3，但其中之一的体积应该是有限的。该问题的局部（时间）唯一可解性是在函数的 Sobolev-Slobodetskii 空间中获得的。详细考虑斯托克斯方程模型问题解的估计，流体之间的界面是平面。 Schauder 方法用于研究具有紧凑边界的线性问题。非线性问题的过渡是通过逐次逼近完成的。
This work solves the problem governing the simultaneous motion of two viscous liquids of different kinds: compressible and incompressible. The boundary between the fluids is considered as an unknown (free) interface where the surface tension is taken into account. Although the fluids occupy the whole space R3, one of them should have a finite volume. Local (in time) unique solvability of this problem is obtained in the Sobolev–Slobodetskii spaces of functions. Estimates of the solution of a model problem for the Stokes equations are considered in detail, the interface between the fluids being a plane. The Schauder method is used to study a linear problem with a compact boundary. The passage to the nonlinear problem is made by successive approximations.