well-posed Cauchy problems and symmetrizability of first order systems
Guy Métivier (2014)
Journal de l’École polytechnique — Mathématiques
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The Cauchy problem for first order system is known to be well-posed in when it admits a microlocal symmetrizer which is smooth in and Lipschitz continuous in . This paper contains three main results. First we show that a Lipschitz smoothness globally in is sufficient. Second, we show that the existence of symmetrizers with a given smoothness is equivalent to the existence of having the same smoothness. This notion was first introduced in []. This is the key point to prove...