On the Cauchy Problem for Axi-Symmetric Vortex Rings

被引：0
作者：
Hao Feng
Vladimír Šverák
机构：
[1] University of Minnesota,
来源：
Archive for Rational Mechanics and Analysis | 2015年 / 215卷
关键词：
Vorticity; Cauchy Problem; Stokes Equation; Biot; Vortex Ring;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We consider the classical Cauchy problem for the three dimensional Navier–Stokes equation with the initial vorticity ω0 concentrated on a circle, or more generally, a linear combination of such data for circles with common axis of symmetry. We show that natural approximations of the problem obtained by smoothing the initial data satisfy good uniform estimates which enable us to conclude that the original problem with the singular initial distribution of vorticity has a solution. We impose no restriction on the size of the initial data.
引用
收藏
页码：89 / 123
页数：34
相关论文
共 29 条
  • [1] Ben-Artzi M.(1994)Global solutions of two-dimensional Navier–Stokes and Euler equations Arch. Ration. Mech. Anal. 128 329-358
  • [2] Cottet G.-H.(1986)Equations de Navier–Stokes dans le plan avec tourbillon initial mesure C. R. Acad. Sci. Paris Ser. I Math. 303 105-108
  • [3] Fabes E.B.(1986)A new proof of Moser’s parabolic Harnack inequality using the old ideas of Nash Arch. Ration. Mech. Anal. 96 327-338
  • [4] Stroock D.W.(2005)On the uniqueness of the solution of the two-dimensional Navier–Stokes equation with a Dirac mass as initial vorticity Math. Nachr. 278 1665-1672
  • [5] Gallagher I.(2005)Global stability of vortex solutions of the two-dimensional Navier–Stokes equation Commun Math. Phys. 255 97-129
  • [6] Gallay Th.(2005)Uniqueness for the two-dimensional Navier–Stokes equation with a measure as initial vorticity Math. Ann. 332 287-327
  • [7] Lions P.-L.(1988)Two-dimensional Navier–Stokes flow with measures as initial vorticity Arch. Ration. Mech. Anal. 104 223-250
  • [8] Gallay Th.(1989)Navier–Stokes flow in R3 with measures as initial vorticity and Morrey spaces Commun. Partial Differ. Equ. 14 577-618
  • [9] Wayne C.E.(1994)The Navier–Stokes equation for an incompressible fluid in R2 with a measure as the initial vorticity Differ. Integral Equ. 7 949-966
  • [10] Gallagher I.(2001)Well-posedness for the Navier–Stokes equations Adv. Math. 157 22-35
123