On 2D Euler Equations: III. A Line Model

2002/06/26 by Yanguang Charles Li, Li, Yanguang Charles
Engineering · Mathematics · Physics and Astronomy · #35 #76 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Spectral Theory (math.SP) #math-ph #math.AP #math.DS #math.FA #math.MP #math.SP #msc:35 #msc:76

paper · pdf · doi:10.48550/arxiv.math/0206278

arxiv created 2002/06/26 · openalex publication_date 2002/06/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The spectral theorem of the linear 2D Euler operator in Sobolev spaces is presented as a corollary of the spectral theorem in ℓ₂ space in [Li,00]. Study on the (dashed) line model introduced in [Li,01] is continued. Specifically, invariant manifolds for the line model is established. The corresponding line model for 2D Navier-Stokes equation is also introduced.

Related

• On 2D Euler Equations: Part II. Lax Pairs and Homoclinic Structures
• Essential spectrum of the linearized 2D Euler equation and Lyapunov-Oseledets exponents
• The Spectrum of a linearized 2D Euler operator
• The Essential Spectrum of the Linearized 2D Euler Operator is a Vertical Band
• Construction of High Regularity Invariant Measures for the 2D Euler Equations and Remarks on the Growth of the Solutions