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  1. Journal of Mathematical Fluid Mechanics
  2. Journal of Mathematical Fluid Mechanics : Volume 8
  3. Journal of Mathematical Fluid Mechanics : Volume 8, Issue 4, December 2006
  4. The Linearized Crocco Equation
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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 8, Issue 4, December 2006
Obituary
Navier–Stokes Equations with First Order Boundary Conditions
Spectral stability of wave trains in the Kawahara equation
The Linearized Crocco Equation
Existence of Solutions with the Prescribed Flux of the Navier–Stokes System in an Infinite Cylinder
2D Slightly Compressible Ideal Flow in an Exterior Domain
Journal of Mathematical Fluid Mechanics : Volume 8, Issue 3, August 2006
Journal of Mathematical Fluid Mechanics : Volume 8, Issue 2, April 2006
Journal of Mathematical Fluid Mechanics : Volume 8, Issue 1, February 2006
Journal of Mathematical Fluid Mechanics : Volume 7
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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The Linearized Crocco Equation

Content Provider SpringerLink
Author Buchot, J. M. Raymond, J. P.
Copyright Year 2006
Abstract In this paper, we study the existence and uniqueness of a degenerate parabolic equation, with nonhomogeneous boundary conditions, coming from the linearization of the Crocco equation [12]. The Crocco equation is a nonlinear degenerate parabolic equation obtained from the Prandtl equations with the so-called Crocco transformation. The linearized Crocco equation plays a major role in stabilization problems of fluid flows described by the Prandtl equations [5]. To study the infinitesimal generator associated with the adjoint linearized Crocco equation – with homogeneous boundary conditions – we first study degenerate parabolic equations in which the x-variable plays the role of a time variable. This equation is doubly degenerate: the coefficient in front of ∂x vanishes on a part of the boundary, and the coefficient of the elliptic operator vanishes in another part of the boundary. This makes very delicate the proof of uniqueness of solution. To overcome this difficulty, a uniqueness result is first obtained for an equation in which the elliptic operator is symmetric, and it is next extended to the original equation by combining an iterative process and a fixed point argument (see Th. 4.9). This kind of argument is also used to prove estimates, which cannot be obtained in a classical way.
Ending Page 541
Page Count 32
Starting Page 510
File Format PDF
ISSN 14226928
e-ISSN 14226952
Journal Journal of Mathematical Fluid Mechanics
Issue Number 4
Volume Number 8
Language English
Publisher Birkhäuser-Verlag
Publisher Date 2006-08-19
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword linearized Crocco equation Mechanics, Fluids, Thermodynamics Degenerate parabolic equation Mathematical Methods in Physics Fluids boundary layer equations Boundary-layer theory, separation and reattachment, higher-order effects Degenerate parabolic equations PDEs in connection with fluid mechanics
Content Type Text
Resource Type Article
Subject Applied Mathematics Mathematical Physics Condensed Matter Physics Computational Mathematics
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