𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Regularity of the global attractor for the Klein–Gordon–Schrödinger equation

✍ Scribed by Horst Lange; Bixiang Wang

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
147 KB
Volume
22
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

This paper deals with the regularity of the global attractor for the Klein}Gordon}Schro K dinger equation. Using a decomposition method, we prove that the global attractor for the one-dimensional model consists of smooth functions provided the forcing terms are regular.

📜 SIMILAR VOLUMES

Classical Global Solutions for Non-linea
Classical Global Solutions for Non-linear Klein–Gordon–Schrödinger Equations
✍ Baoxiang Wang 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 326 KB

The existence of the classical global solutions for the non-linear Klein-Gordon-Schro¨dinger equations is proved in H-subcritical cases for space dimensions n)5. For higher space dimensions 6)n)9, we will give a subsequent paper to deal with.

On the Whitham equations for the semicla
On the Whitham equations for the semiclassical limit of the defocusing nonlinear Schrödinger equation
✍ Fei-Ran Tian; Jian Ye 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 448 KB 👁 2 views

We study the Whitham equations, which describe the semiclassical limit of the defocusing nonlinear Schrödinger equation. The limit is governed by a pair of hyperbolic equations of two independent variables for a short time starting from the initial time. After this hyperbolic solution breaks down, t

On weakly convergent sequences in Banach
On weakly convergent sequences in Banach function spaces and the initial-boundary value problems for non-linear Klein–Gordon–Schrödinger equations
✍ Wang Baoxiang 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 123 KB 👁 2 views

In the paper, we shall prove that almost everywhere convergent bounded sequence in a Banach function space X is weakly convergent if and only if X and its dual space X\* have the order continuous norms. It follows that almost everywhere convergent bounded sequence in ¸N #¸N (1(p , p (R) is weakly co

On blowup for the pseudo-conformally inv
On blowup for the pseudo-conformally invariant nonlinear Schrödinger equation II
✍ Hayato Nawa; Masayoshi Tsutsumi 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 96 KB

We study the δ-measure-like blowup of solutions to the pseudo-conformally invariant nonlinear Schrödinger equation For N = 1 or N ≥ 2 and u0 radially symmetric, we prove that if the blowup solution u(t) satisfies |u(t, x)| 2 dx u0 2 δ0(dx) in the sense of measures as t ↑ Tm (i.e., weakly \* in B ,

Linear Boltzmann equation as the weak co
Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation
✍ László Erdős; Horng-Tzer Yau 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 392 KB

We study the time evolution of a quantum particle in a Gaussian random environment. We show that in the weak coupling limit the Wigner distribution of the wave function converges to a solution of a linear Boltzmann equation globally in time. The Boltzmann collision kernel is given by the Born approx