On the global strong solutions of coupled Klein-Gordon-Schrödinger equations
Nakao Hayashi,Wolf von Wahl +1 more
TLDR
On considere le systeme suivant d'equations a 3 dimensions d'espace: idψ/dt-A 1 ψ=−ψφ, d 2 φ/dt 2 +A 2 π=|ψ| 2, Ou A 1 and A 2 sont des operateurs elliptiques autoadjoints positifs d'ordre 2 avec des conditions de Dirichlet nulles sur un domaine borne or non borne Ω⊂R 3.Abstract:
On considere le systeme suivant d'equations a 3 dimensions d'espace: idψ/dt-A 1 ψ=−ψφ, d 2 φ/dt 2 +A 2 φ=|ψ| 2 . Ou A 1 et A 2 sont des operateurs elliptiques autoadjoints positifs d'ordre 2 avec des conditions de Dirichlet nulles sur un domaine borne ou non borne Ω⊂R 3 . On demontre l'existence de solutions globales fortesread more
Citations
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Limiting case of the Sobolev inequality in BMO, with application to the Euler equations
Hideo Kozono,Yasushi Taniuchi +1 more
TL;DR: In this paper, a logarithmic Sobolev inequality by means of the BMO-norm in the critical exponents of the Euler equation was proved, and a blow-up criterion of solutions to Euler equations was established.
Journal ArticleDOI
Efficient and accurate numerical methods for the Klein-Gordon-Schrödinger equations
Weizhu Bao,Li Yang +1 more
TL;DR: These numerical methods for approximations of the Klein-Gordon-Schrodinger (KGS) equations with/without damping terms are efficient, unconditionally stable and accurate, and of spectral accuracy in space and second-order accuracy in time.
Journal ArticleDOI
Convergence of a conservative difference scheme for a class of Klein-Gordon-Schrödinger equations in one space dimension
TL;DR: A conservative difference scheme is presented for the initial-boundary value problem of a class of Klein-Gordon-Schrodinger equations and convergence of the difference solution is proved with order O(h^2+@t^2) in the energy norm.
Journal ArticleDOI
Attractor for Dissipative Klein–Gordon–Schrödinger Equations inR3
Guo Boling,Li Yongsheng +1 more
TL;DR: In this article, the authors considered the Cauchy problem of coupled dissipative Klein-Gordon-Schrodinger equations in R 3 and proved the existence of the maximal attractor.
Journal ArticleDOI
Global Attractors for the Klein-Gordon-Schrödinger Equation in Unbounded Domains
TL;DR: In this article, the authors studied the long time behavior of solutions for the Klein-Gordon-Schrodinger equation in the whole space R n with n⩽3 and proved the continuity of the solutions on initial data and established the asymptotic compactness of solutions.
References
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A note on limiting cases of sobolev embeddings and convolution inequalities
Haim Brezis,Stephen Wainger +1 more
TL;DR: In this paper, a note on limiting cases of sobolev embeddings and convolution inequalities is given, along with a discussion of the relation between the two types of embedding.
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Philip Brenner,Wolf von Wahl +1 more
TL;DR: In this paper, the homogeneous initial-boundary value problem over IR+ x f2 for a smooth open set was studied and a strong solution of (0.1) was shown to exist.
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Problème de Cauchy pour des systèmes hyperboliques semi-linéaires
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The Cauchy Problem for the Coupled Schroedinger-Klein-Gordon Equations
J.B. Baillon,John M. Chadam +1 more
TL;DR: In this article, the authors considered the Cauchy problem for the closely related coupled Schoredinger-Klein-Gordon (SKG) equations and showed the existence of a unique global solution for the SKG equation in the space ∑ 2.
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