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Time-dependent loss of derivatives for hyperbolic operators with non regular coefficients (1305.1095v1)
Published 6 May 2013 in math.AP
Abstract: In this paper we will study the Cauchy problem for strictly hyperbolic operators with low regularity coefficients in any space dimension $N\geq1$. We will suppose the coefficients to be log-Zygmund continuous in time and log-Lipschitz continuous in space. Paradifferential calculus with parameters will be the main tool to get energy estimates in Sobolev spaces and these estimates will present a time-dependent loss of derivatives.