LOCAL WELL-POSEDNESS OFNONLOCAL BURGERS EQUATIONS

SYLVIE BENZONI-GAVAGE

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LOCAL WELL-POSEDNESS OFNONLOCAL BURGERS EQUATIONS

机译：非局部伯格方程的局部适定性

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This paper is concerned with nonlocal generalizations ofthe inviscid Burgers equation arising as amplitude equations for weaklynonlinear surface waves. Under homogeneity and stability assumptionson the involved kernel it is shown that the Cauchy problem is locally wellposed in H~2(R), and a blow-up criterion is derived. The proof basedon a priori estimates without loss of derivatives, and on a regularizationof both the equation and the initial data.

机译：本文涉及无粘性的Burgers方程的非局部推广，它是弱非线性表面波的振幅方程。在均匀性和稳定性假设下，所涉及的核表明，柯西问题在H〜2（R）中局部存在，并推导了爆破准则。该证明基于先验估计而没有导数损失，并且基于等式和初始数据的正则化。

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来源
《Differential and integral equations》 |2009年第4期|共18页
作者
SYLVIE BENZONI-GAVAGE;
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原文格式 PDF
正文语种 eng
中图分类微分方程、积分方程;
关键词
Burgers equation; stability; regularization;

机译：Burgers方程;稳定性;正则化;

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1. LOCAL WELL-POSEDNESS OFNONLOCAL BURGERS EQUATIONS [J] . SYLVIE BENZONI-GAVAGE Differential and integral equations . 2009,第3a4期

机译：非局部伯格方程的局部适定性
2. Local and global well-posedness for the 2D Zakharov-Kuznetsov-Burgers equation in low regularity Sobolev space [J] . Hirayama Hiroyuki Journal of Differential Equations . 2019,第7期

机译：在低规律性SoboLev空间中的2D Zakharov-Kuznetsov-Burgers方程的本地和全球良好良好
3. Local well-posedness and ill-posedness for the fractal Burgers equation in homogeneous Sobolev spaces [J] . Xu XJ Mathematical Methods in the Applied Sciences . 2009,第3期

机译：齐次Sobolev空间中分形Burgers方程的局部适定性和不适定性
4. Dynamical difference between nonlocal and local burgers equations [C] . Jinqiao Duan, Xin-Chu Fu, Eric Lowenstein, International conference on nonlinear mechanics . 1998

机译：非局部和局部汉堡和局部方程之间的动态差异
5. Unique continuation for parabolic equations and local well-posedness of mKdV equation [D] . Nguyen, Tu Anh 2008

机译：抛物线方程的唯一延续和mKdV方程的局部适定性
6. Viscosity-dependent inertial spectra of the Burgers and Korteweg–deVries–Burgers equations [O] . Alexandre J. Chorin, Ole H. Hald 2005

机译：Burgers和Korteweg-deVries-Burgers方程的与粘度有关的惯性谱
7. Local Well-posedness of A Non-local Burgers Equation [O] . Yang, Hang, Goodchild, Sam 2013

机译：非局部Burgers方程的局部适定性

LOCAL WELL-POSEDNESS OFNONLOCAL BURGERS EQUATIONS

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