二维不可压缩欧拉方程连续模的损失与传播

IF 1.7 2区 数学 Q1 MATHEMATICS
Karim R. Shikh Khalil
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引用次数: 0

摘要

从科赫的工作中得知,二维不可压缩欧拉方程传播涡度的迪尼连续模。在这项工作中,我们考虑具有涡度连续模的二维欧拉方程比迪尼连续更粗糙。我们首先证明了二维欧拉方程传播的涡度连续模的显式族比迪尼连续性粗糙。这项工作的主要目标是解决以下问题:给定二维欧拉方程的连续模,我们是否总是传播它?这个问题的答案是否定的。我们构造了非传播二维欧拉方程的连续模族。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the loss and propagation of modulus of continuity for the two-dimensional incompressible Euler equations
It is known from the work of Koch that the two-dimensional incompressible Euler equations propagate Dini modulus of continuity for the vorticity. In this work, we consider the two-dimensional Euler equations with a modulus of continuity for vorticity rougher than Dini continuous. We first show that the two-dimensional Euler equations propagate an explicit family of moduli of continuity for the vorticity that are rougher than Dini continuity. The main goal of this work is to address the following question: Given a modulus of continuity for the 2D Euler equations, can we always propagate it? The answer to this question is No. We construct a family of moduli of continuity for the 2D Euler equations that are not propagated.
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来源期刊
CiteScore
3.20
自引率
5.90%
发文量
271
审稿时长
7.5 months
期刊介绍: The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis
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