This number of unique articles and surveys, rising from a 2011 convention in Bertinoro, Italy, addresses contemporary advances in linear and nonlinear elements of the speculation of partial differential equations (PDEs). part area research equipment, sometimes called microlocal research, have persevered to yield notable effects over the last years and are actually one of many major instruments of research of PDEs. Their position in lots of functions to physics, together with quantum and spectral concept, is both important.Key issues addressed during this quantity include:*general conception of pseudodifferential operators*Hardy-type inequalities*linear and non-linear hyperbolic equations and systems*Schrödinger equations*water-wave equations*Euler-Poisson systems*Navier-Stokes equations*heat and parabolic equationsVarious degrees of graduate scholars, in addition to researchers in PDEs and comparable fields, will locate this booklet to be a great resource.ContributorsT. Alazard                                P.I. NaumkinJ.-M. Bony                              F. Nicola N. Burq                                   T. NishitaniC. Cazacu                                T. OkajiJ.-Y. Chemin                           M. PaicuE. Cordero                              A. ParmeggianiR. Danchin                               V. PetkovI. Gallagher                              M. ReissigT. Gramchev                            L. RobbianoN. Hayashi                               L. RodinoJ. Huang                                  M. Ruzhanky   D. Lannes                                J.-C. SautF. Linares                                N. ViscigliaP.B. Mucha                             P. ZhangC. Mullaert                              E. ZuazuaT. Narazaki                             C. Zuily