Global existence for coupled Klein-Gordon equations with different speeds

Pierre Germain

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We study the simultaneous linearizability of $d$ –actions (and the corresponding $d$ -dimensional Lie algebras) defined by commuting singular vector fields in $ℂ^{n}$ fixing the origin with nontrivial Jordan blocks in the linear parts. We prove the analytic convergence of the formal linearizing transformations under a certain invariant geometric condition for the spectrum of $d$ vector fields generating a Lie algebra. If the condition fails and if we consider the situation where small denominators...

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Existence of strong solutions for nonisothermal Korteweg system

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This work is devoted to the study of the initial boundary value problem for a general non isothermal model of capillary fluids derived by J. E Dunn and J. Serrin (1985) in [9, 16], which can be used as a phase transition model. We distinguish two cases, when the physical coefficients depend only on the density, and the general case. In the first case we can work in critical...