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  1. Journal of Mathematical Fluid Mechanics
  2. Journal of Mathematical Fluid Mechanics : Volume 7
  3. Journal of Mathematical Fluid Mechanics : Volume 7, Issue 3, Supplement,August 2005
  4. Microglobal Analysis of the Euler Equations
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Journal of Mathematical Fluid Mechanics : Volume 19
Journal of Mathematical Fluid Mechanics : Volume 18
Journal of Mathematical Fluid Mechanics : Volume 17
Journal of Mathematical Fluid Mechanics : Volume 16
Journal of Mathematical Fluid Mechanics : Volume 15
Journal of Mathematical Fluid Mechanics : Volume 14
Journal of Mathematical Fluid Mechanics : Volume 13
Journal of Mathematical Fluid Mechanics : Volume 12
Journal of Mathematical Fluid Mechanics : Volume 11
Journal of Mathematical Fluid Mechanics : Volume 10
Journal of Mathematical Fluid Mechanics : Volume 9
Journal of Mathematical Fluid Mechanics : Volume 8
Journal of Mathematical Fluid Mechanics : Volume 7
Journal of Mathematical Fluid Mechanics : Volume 7, Issue 4, November 2005
Journal of Mathematical Fluid Mechanics : Volume 7, Issue 3, Supplement,August 2005
Topics in an Ideal Fluid Dynamics
Solutions with Concentration to the Riemann Problem for the One-Dimensional Chaplygin Gas Equations
Regularity in an Unusual Variational Problem
Existence of Multimodal Standing Gravity Waves
Asymptotic Directions, Monge–Ampère Equations and the Geometry of Diffeomorphism Groups
On Stability of a Regular Vortex Polygon in the Circular Domain
Microglobal Analysis of the Euler Equations
On Vibrodynamics of Pendulum and Submerged Solid
Journal of Mathematical Fluid Mechanics : Volume 7, Issue 3, August 2005
Journal of Mathematical Fluid Mechanics : Volume 7, Issue 2, Supplement,May 2005
Journal of Mathematical Fluid Mechanics : Volume 7, Issue 2, May 2005
Journal of Mathematical Fluid Mechanics : Volume 7, Issue 1, Supplement,March 2005
Journal of Mathematical Fluid Mechanics : Volume 7, Issue 1, March 2005
Journal of Mathematical Fluid Mechanics : Volume 6
Journal of Mathematical Fluid Mechanics : Volume 5
Journal of Mathematical Fluid Mechanics : Volume 4
Journal of Mathematical Fluid Mechanics : Volume 3
Journal of Mathematical Fluid Mechanics : Volume 2
Journal of Mathematical Fluid Mechanics : Volume 1

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Microglobal Analysis of the Euler Equations

Content Provider SpringerLink
Author Shnirelman, Alexander
Copyright Year 2005
Abstract The flow of the ideal incompressible fluid can be regarded as the motion along a geodesic on the group of volume preserving diffeomorphisms of the flow domain. Thus, we can define the exponential map transferring the initial velocity (an incompressible vector field tangent to the boundary) into the fluid configuration at the time one. In the 2-d case this map is defined globally (for all initial velocities) and smooth. Recently Ebin, Misiołlek and Preston [EMP] have proved that the exponential map is Fredholm. In this paper a stronger result is proved: the exponential map is Fredholm quasiruled (FQR), i.e. has a rigid global structure. The proof uses some simplified tools of paradifferential calculus.
Ending Page S396
Starting Page S387
File Format PDF
ISSN 14226928
e-ISSN 14226952
Journal Journal of Mathematical Fluid Mechanics
Issue Number 3
Volume Number 7
Language English
Publisher Birkhäuser-Verlag
Publisher Date 2005-01-01
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Mechanics, Fluids, Thermodynamics Mathematical Methods in Physics Fluids group of diffeomorphisms Fredholm maps paradifferential operators Ideal incompressible fluid Stability and instability of nonparallel flows Existence, uniqueness, and regularity theory
Content Type Text
Resource Type Article
Subject Applied Mathematics Mathematical Physics Condensed Matter Physics Computational Mathematics
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