Global existence for systems of nonlinear wave equations in two space dimensions. II
type: Item
instance of: scholarly article
title: Global existence for systems of nonlinear wave equations in two space dimensions. II
zbMATH Open document ID: 0864.35075
author: Soichiro Katayama
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1997-06-15T00:00:00Z
review text: [For part I see Zbl 0830.35083.] The author considers the Cauchy problem for the system of nonlinear wave equations \[ (\partial^2_t-\Delta)u_i= F_i(u,u',u'') \qquad\text{in}\quad (0,\infty)\times\mathbb{R}^2, \quad i=1,\dots,N, \] with initial data \(u_i(0,x)= \varepsilon\phi_i\), \(\partial_t u_i(0,x)=\varepsilon \psi_i(x)\), where \(F_i\) are smooth functions of degree 3 near the origin \((u,u',u'')=0\), \(\phi_i,\psi_i\in C_0^\infty(\mathbb{R}^2)\), and \(\varepsilon\) is a small positive parameter. \(F_i\) are assumed to be independent of \(u_j''\) for any \(j\neq i\). The author also discussed such a Cauchy problem in his previous paper. But in this paper, he alleviates the restriction of his conclusion and obtains the global existence provided that Klainerman's null condition on the cubic part of the nonlinear terms is satisfied.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35L15
zbMATH DE Number: 878494
zbMATH Keywords: null condition
reviewed by: Shuxing Chen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195163919
OpenAlex ID: W4245720956
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DOI: 10.2977/PRIMS/1195163919
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description: scientific article; zbMATH DE number 878494