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Advances in Phase Space Analysis of Partial Differential Equations

This collection of original articles and surveys addresses the recent advances in linear and nonlinear aspects of the theory of partial differential equations.

Key topics:

* Operators as "sums of squares" of real and complex vector fields:both analytic hypoellipticity and regularity for very low regularity coefficients;

* Nonlinear evolution equations: Navier–Stokes system, Strichartz estimates for the wave equation, instability and the Zakharov equation and eikonals;

* Local solvability: its connection with subellipticity, local solvability for systems of vector fields in Gevrey classes;

* Hyperbolic equations: the Cauchy problem and multiple characteristics, both positive and negative results.

Graduate students at various levels as well as researchers in PDEs and related fields will find this an excellent resource.

Contributors: Ambrosio, Berhanu, J.-M. Bony, Chemin, Dencker, Gallagher, Gerard, Hounie, Jannelli, Kajitani, Lerner, Nishitani, Petkov, Rauch, Reissig, Spagnolo, Tataru, Treves, Uhlmann, and Zuazua.

Common terms and phrases

algebra approximation property assume assumption belongs Besov spaces bicharacteristic boundary bounded Cauchy problem coefficients commutative condition consider continuous damped defined Definition denote derivatives Differential Equations eigenvalues Example exists exponential decay finite loss finite type Fourier integral operators Fourier transform frequency localized function Heisenberg group hence holomorphic homogeneous hyperbolic equations hyperbolic operators inequality invariant invertible kernel KerQ Lebesgue measure Lemma linear localized energy estimates locally solvable loss of regularity Math matrix metric multiplicity neighborhood nondegenerate norm obtain one-dimensional orbits ordinary reflecting partial differential Phase Space Analysis polynomial positive constant principal symbol principal type proof of Theorem Proposition prove pseudodifferential operators quasi-symmetrizable real analytic Remark result scalar Section sequence Sobolev spaces solution Springer Science+Business Media Strichartz estimates subelliptic symmetrizer Theorem 1.1 vanishes vector field viscosity viscosity operator wave equation weakly hyperbolic well-posed zero

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