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In this paper we present a comprehensive treatment of function spaces with logarithmic
smoothness (Besov, Sobolev, Triebel-Lizorkin). We establish the following results: Sharp …

The aim of the paper is to establish (local) optimal embeddings of Besov spaces B p, r 0, b
involving only a slowly varying smoothness b. In general, our target spaces are outside of …

In this paper we continue the analysis of non-diagonalisable hyperbolic systems initiated in
[,]. Here we assume that the system has discontinuous coefficients or more in general …

We consider an abstract wave equation with a propagation speed that depends only on
time. We investigate well-posedness results with finite derivative loss in the case where the …

This paper considers a family of active scalar equations which modify the generalized
surface quasi-geostrophic (gSQG) equations through its constitutive law or dissipative …

We consider an abstract wave equation with a propagation speed that depends only on
time. We assume that the propagation speed is differentiable for positive times, continuous …

We investigate the behavior of the solutions of a class of certain strictly hyperbolic equations
defined on [0, T]× R n in relation to a class of metrics on the phase space. In particular, we …

In the present paper, we consider second order strictly hyperbolic linear operators of the
form $ Lu\,=\,\partial_t^ 2u\,-\,{\rm div}\big (A (t, x)\nabla u\big) $, for $(t, x)\in [0 …

The present paper concerns the well-posedness of the Cauchy problem for microlocally
symmetrizable hyperbolic systems whose coefficients and symmetrizer are log-Lipschitz …