Concentrations in regularizations for 2-D incompressible flow
Concentrations in regularizations for 2-D incompressible flow
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DOI：
10.1002/cpa.3160400304
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发表时间：
1987-05
影响因子：
3
通讯作者：
R. J. Diperna;A. Majda
中科院分区：
文献类型：
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作者：
R. J. Diperna;A. Majda
无粘不可压缩二维流体流动的欧拉方程由xE R*，t> 0给出，其中u=（u1，u2）是流体速度，p是标量压力，Du/Dt= Au/at+（uV）U，uo是初始不可压缩速度场，即div uo= 0。数学流体动力学中的一个开放问题，从理论和应用的角度来看，（见[22]，[16]）是具有以下结构的初始数据的无粘二维Euler方程弱解的存在性和结构：初始涡度，oo=旋度uo，是一个Radon测度，而初始速度具有局部有限动能，即，这样的初始数据出现在涡面的演化过程中。有一个广泛应用的数学文献，主要是基于数值计算和形式渐近方法，分析了初始数据满足（0.2）的欧拉方程的解的演化（见文献[22]，[20]）。从严格的角度来看，涡面定义了一个经典的不适定问题，大部分工作都涉及通过非线性柯西-科瓦列斯基定理（见[7]，[23]）的有限时间间隔的解析涡面的存在性定理。最近，已经证明（见[13]），对于均匀涡面的任何适当的小振幅扰动，存在一个特殊的解析解。
The Euler equations for an inviscid incompressible 2-D fluid flow are given by x E R*, t> 0, where u=(ul, u2) is the fluid velocity, p is the scalar pressure, Du/Dt= au/at+(u V) U, and uo is an initial incompressible velocity field, ie, div uo= 0. An open problem in mathematical fluid dynamics with wide current interest from both the theoretical and applied viewpoints (see [22],[16]) is the existence and structure of weak solutions to the inviscid two-dimensional Euler equations for initial data with the following structure: The initial vorticity, oo= curl uo, is a Radon measure while the initial velocity has locally finite kinetic energy, ie, Such initial data arises in the evolution of vortex sheets. There is a wide applied mathematical literature based mostly on numerical calculations and formal asymptotic methods which analyzes the evolution of solutions of the Euler equations with initial data satisfying (0.2)(see the bibliography in [22],[20]). From the rigorous point of view, vortex sheets define a classical ill-posed problem and most of the work has involved existence theorems for analytic vortex sheets for finite-time intervals through nonlinear Cauchy-Kowaleski theorems (see [7],[23]). Recently, it has been proved (see [13]) that given any appropriate small amplitude perturbation of a uniform vortex sheet, there is one special analytic