Solvability in weighted Hölder spaces for a problem governing the evolution of two compressible fluids
Solvability in weighted Hölder spaces for a problem governing the evolution of two compressible fluids
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控制两种可压缩流体演化问题在加权霍尔德空间中的可解性
DOI：
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发表时间：
2005
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通讯作者：
I. Denisova
中科院分区：
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作者：
I. Denisova
在无穷远处具有幂函数衰减的Hölder空间中，得到了两种体积有限的可压缩流体运动问题的局部（时间上）唯一可解性。通过拉格朗日坐标系，我们得到了一个具有给定液体间闭合界面的非线性初边值问题。在线性化问题可解的基础上，利用不动点定理建立了该问题的存在性定理。为了得到估计并证明线性化问题的可解性，我们使用Schauder方法和一个具有平面界面的模型线性问题的显式解。结果是在一定的流体密度和粘度限制下得到的，这意味着流体之间的差异不大。参考书目：8篇。
Local (in time) unique solvability of a problem on the motion of two compressible fluids, one of which has finite volume, is obtained in Hölder spaces of functions with a power-like decay at infinity. After passage to Lagrangian coordinates, we arrive at a nonlinear initial boundary value problem with a given closed interface between the liquids. We establish an existence theorem for this problem on the basis of the solvability of a linearized problem by means of the fixed-point theorem. To obtain estimates and to prove the solvability for the linearized problem, we use the Schauder method and an explicit solution of a model linear problem with a plane interface between the liquids. The results are obtained under some restrictions on the fluid density and viscosities, which mean that the fluids are not much different from each other. Bibliography: 8 titles.