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有读书笔记有附件Remarks on the breakdown of smooth solutions for the 3-D Euler equations

热1 yhhuang 添加于 2010-02-01 10:37

  •  作 者

    Beale JT, Kato T, Majda A

  •  摘 要

    The authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3-D Euler equations. In other words, if a solution of the Euler equations is initially smooth and loses its regularity at some later time, then the maximum vorticity necessarily grows without bound as the critical time approaches; equivalently, if the vorticity remains bounded, a smooth solution persists.
Partially supported by O.N.R. Contract No. N00014-76-C-0316 and N.S.F. Grant No. MCS-81-01639

  •  详细资料

    • 文献种类: Journal Article
    • 期刊名称: Communications in Mathematical Physics
    • 期刊缩写: Commun.Math. Phys.
    • 期卷页: 1984年  第94卷 第1期 61-66页
    • ISBN: 0010-3616

  • 学科领域 自然科学 » 数学

  •  标 签

    blowup Euler Equation weak solution 

  • 相关链接 DOI URL 

  •  附 件

    PDF附件Notes  PDF附件The original article 

  •  yhhuang 的文献笔记  订阅

    This paper has far-reaching impact in two aspects:

    1. The control of blow-up of higer norms in terms of lower norms. In general, we know that the blowup for Euler equation is in space Hs for s >= 3 in three dimension. This paper shows that the blowup of this norm is accampanied by the infinite norm of the vorticity. The results are generalized to other systems like MHD equations and Euler-Poisson equations
    2. This privide a guide for the search of singularity by numerical methods. Therefore, it is much easier to monitor ||ω||∞  for blowup than computing the Hsnorm of the velocity.
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