Table Of ContentSpringer INdAM Series 17
Ferruccio Colombini
Daniele Del Santo
David Lannes Editors
Shocks, Singularities
and Oscillations in
Nonlinear Optics and
Fluid Mechanics
Springer INdAM Series
Volume 17
Editor-in-Chief
G.Patrizio
SeriesEditors
C.Canuto
G.Coletti
G.Gentili
A.Malchiodi
P.Marcellini
E.Mezzetti
G.Moscariello
T.Ruggeri
Moreinformationaboutthisseriesathttp://www.springer.com/series/10283
Ferruccio Colombini • Daniele Del Santo (cid:129)
David Lannes
Editors
Shocks, Singularities
and Oscillations in Nonlinear
Optics and Fluid Mechanics
123
Editors
FerruccioColombini DanieleDelSanto
DipartimentodiMatematica DipartimentodiMatematicaeGeoscienze
UniversitaJdiPisa UniversitaJdiTrieste
Pisa,Italy Trieste,Italy
DavidLannes
InstitutdeMathématiquesdeBordeaux
UniversitédeBordeaux-UMR5251
Talence,France
ISSN2281-518X ISSN2281-5198 (electronic)
SpringerINdAMSeries
ISBN978-3-319-52041-4 ISBN978-3-319-52042-1 (eBook)
DOI10.1007/978-3-319-52042-1
LibraryofCongressControlNumber:2017939581
©SpringerInternationalPublishingAG2017
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...,così comeraia
da l’un,sesiconosce, ilcinquee’l sei;
Par. XV, 56–57.
Preface
The present volume is a collection of papers with a strong focus on the study of
nonlinear hyperbolic systems, and it addresses general theoretical issues such as
symmetrizability,singularities,lowregularityanddispersiveperturbations.
The past decade has been marked by important breakthroughs in the study of
physicalphenomenawherethetheoryofhyperbolicsystemsplaysacentralrole.We
referinparticulartoresultsinnonlinearoptics,shocktheory,andfluidmechanics.
All these topics are developed in the papers contained in this volume, which also
includestwo thoroughsurveyson importantresearch areas.The first, byL. Saint-
Raymond, is devoted to the derivation of fluid models as hydrodynamiclimits of
themesoscopicBoltzmannequations,whilethesecond,byK.Zumbrun,addresses
recentdevelopmentsindetonationtheory.
Thepapersinthevolumehaveallbeenwrittenbyleadingexpertsintheirrespec-
tive fields. They are expanded versions of talks given at the INDAM Workshop
“Shocks,SingularitiesandOscillationsinNonlinearOpticsandFluidMechanics”,
heldinSeptember2015at IstitutoNazionalediAltaMatematica,Dipartimentodi
Matematica “G. Castelnovo”, University of Rome “La Sapienza”. The workshop
was organized in honor of Guy Métivier, on the occasion of his 65th birthday: it
is our pleasure to dedicate to him this volume, to which a number of friends and
collaboratorspromptlymanifestedtheirwillingnesstocontribute.
Wewouldliketotakethisopportunitytothankallthecontributorsaswellasthe
participantsintheworkshop.
The Istituto Nazionale di Alta Matematica “Francesco Severi” and the GDR
CNRS2434madeitpossibletoholdtheworkshopthroughtheirfinancialsupport.
Wewarmlythankthemfortheirgenerosity.
Pisa,Italy FerruccioColombini
Trieste,Italy DanieleDelSanto
Talence,France DavidLannes
vii
Contents
AmplitudeEquationsforWeaklyNonlinearSurfaceWaves
inVariationalProblems ......................................................... 1
SylvieBenzoni-GavageandJean-FrançoisCoulombel
GlobalWeakSolutionsofPDEsforCompressibleMedia:
ACompactnessCriteriontoCoverNewPhysicalSituations................ 33
DidierBreschandPierre-EmmanuelJabin
Second Microlocalizationand Stabilizationof Damped Wave
EquationsonTori ................................................................ 55
NicolasBurq
AFewRemarksonHyperbolicSystemswithZygmund
inTimeCoefficients.............................................................. 75
FrancescoFanelli
WellposednessofLinearizedTaylorEquations
inMagnetohydrodynamics...................................................... 103
IsabelleGallagherandDavidGérard-Varet
StrictlyDissipativeNonuniquenesswithCorners ............................ 141
GuyMétivierandJeffreyRauch
OntheSolvabilityofCertainDegeneratePartial
DifferentialOperators........................................................... 151
AlbertoParmeggiani
LocationandWeylFormulafor the Eigenvaluesof Some Non
Self-AdjointOperators.......................................................... 181
VesselinPetkov
AMicroscopicPointofViewonSingularitiesinFluidModels ............. 205
LaureSaint-Raymond
ix
x Contents
GeometricOpticsforRayleighPulsesinNonlinearElasticity.............. 261
MarkWilliams
RecentResultsonStabilityofPlanarDetonations........................... 273
KevinZumbrun
Contributors
Sylvie Benzoni-Gavage Institut Camille Jordan (CNRS UMR5208), Université
ClaudeBernardLyon1,VilleurbanneCedex,France
DidierBresch LAMACNRSUMR5127,UniversityofSavoieMont-Blanc,Bat.
LeChablais,Campusscientifique,Chambéry,France
Nicolas Burq Laboratoire de Mathématiques d’Orsay, Université Paris-Sud,
CNRS,OrsayCedex,France
Jean-François Coulombel Laboratoire de Mathématiques Jean Leray, CNRS,
UniversitédeNantes(CNRSUMR6629),NantesCedex3,France
FrancescoFanelli InstitutCamilleJordan–CNRSUMR5208,UniversitéClaude
Bernard–Lyon1,VilleurbanneCedex,France
Isabelle Gallagher Institut de Mathématiques de Jussieu-Paris Rive Gauche,
UniversitéParisDiderot,SorbonneParisCité,ParisCedex13,France
David Gérard-Varet Institut de Mathématiques de Jussieu-Paris Rive Gauche,
UniversitéParisDiderot,SorbonneParisCité,ParisCedex13,France
Pierre-EmmanuelJabin CSCAMMandDepartmentofMathematics,University
ofMaryland,CollegePark,MD,USA
Guy Métivier Institut de Mathématiques de Bordeaux, Université de Bordeaux,
TalenceCedex,France
Alberto Parmeggiani Department of Mathematics, University of Bologna,
Bologna,Italy
VesselinPetkov InstitutdeMathématiquesdeBordeaux,UniversitédeBordeaux,
TalenceCedex,France
JeffreyRauch Departmentof Mathematics, Universityof Michigan,Ann Arbor,
MI,USA
xi
