Titlebook: Studies in Phase Space Analysis with Applications to PDEs; Massimo Cicognani,Ferruccio Colombini,Daniele Del Book 2013 Springer Science+B

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The Water-Wave Equations: From Zakharov to Euler,on of the classical Euler equations. It is proved that these results hold in rough domains, under minimal assumptions on the regularity to ensure, in terms of Sobolev spaces, that the solutions are ...

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On the Characterization of Pseudodifferential Operators (Old and New),boundedness of their iterated commutators. As a corollary, functions of pseudodifferential operators are themselves pseudodifferential. Sufficient conditions are given for the geodesic temperance. In particular, it is valid in the Beals–Fefferman calculus.

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On the Cauchy Problem for Noneffectively Hyperbolic Operators, a Transition Case,hanges across a submanifold of codimension 1 of the double characteristic manifold. Under the assumption that there is no null bicharacteristic tangent to the submanifold where the spectral transition occurs, we derive microlocal a priori estimates assuming the strict Ivrii-Petkov-H?rmander condition.

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Book 2013ear aspects of the theory of partial differential equations (PDEs). Phase space analysis methods, also known as microlocal analysis, have continued to yield striking results over the past years and are now one of the main tools of investigation of PDEs. Their role in many applications to physics, in

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,The Role of Spectral Anisotropy in the Resolution of the Three-Dimensional Navier–Stokes Equations,y in time. The main feature of these initial data is an anisotropic distribution of their frequencies. One of those classes is taken from Chemin and Gallagher (Trans. Am. Math. Soc. 362(6):2859–2873, 2010) and Chemin et al. (J. für die reine und angewandte Mathematik, to appear), and another one is new.

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,The Cauchy Problem for the Euler–Poisson System and Derivation of the Zakharov–Kuznetsov Equation,that the long-wave small-amplitude limit is described by the Zakharov–Kuznetsov equation. This is done first in the case of cold plasma; we then show how to extend this result in presence of the isothermal pressure term with uniform estimates when this latter goes to zero.

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