非线性 KGS 系统强解的范数增长

Abstract

Abstract:

This paper is concerned with the initial-boundary value problem for the nonlinear Klein-Gordon-Schrödinger (KGS) system in $\mathbb{R}^N(N\leq3)$. By introducing a regularized system and utilizing the boundedness and convergence of the solutions sequence, we prove the existence and uniqueness of global strong solutions to the nonlinear KGS system in the space $H^2 \times H^2 \times H^1$, and obtain the norm estimates for the solutions in the space $H^2 \times H^2 \times H^1$. The proof is independent of the Brezis-Gallouet technique and the compactness argument.

Key words: Klein-Gordon-Schr?dinger system, giobal strong solutions, existence and uniqueness, Sobolev norm growth

CLC Number:

O175.29

Shuang Cui, Qihong Shi. On the Norm Growth of Strong Solutions for Nonlinear KGS System[J].Acta mathematica scientia,Series A, 2026, 46(3): 1142-1159.

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References 22

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On the Norm Growth of Strong Solutions for Nonlinear KGS System

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