Index

Q(Y ), partial inverse, 117

A, Wiener algebra, 96

E, restriction of E to quasiperiodic

profiles, 307

Eα(ξ), spectral projection for

αth

sheet,

95

E, 267–275

E, projection onto kernel for

trigonometric series, 306

F, Fourier transform, 45

Hs(Rd), Sobolev space, 46

Hs,

∂ Sobolev space, 278–282

Hs(y), local Sobolev space, 134

Hs(y,

η), microlocal Sobolev space, 137

Lt

qLx,

r Strichartz norms, 111

Op(σ, ∂x), order σ differential

operators, 50

PCk, piecewise smooth functions, 11

Q, restriction of Q to quasiperiodic

profiles, 307

Q(y), partial inverse of L1(y, dφ(y)),

155

Q(α), partial inverse of L1(α), 306

Q, partial inverse for trigonometric

series, 307

Sm(Ω

×

RN

), classical symbols, 181

WF , wavefront set, 139

WFs,

Hs

wavefront set, 137

xξ, 19

π(y, η), spectral projection on

ker L1(y, η), 71

σ-admissible, for Strichartz inequality,

112

Ωt, 271

Ω(t), 271

bicharacteristic

and Hamilton-Jacobi theory, 210

and propagation of singularities,

188–195

and stabilization, 201–205

and transport, 151, 165–166

Borel’s theorem, 128, 151, 229, 270, 313

boundary layer, xv

breakdown/blow up, 224–227, 237–238,

325, 330

Brenner’s theorem, xii, 12, 102–104

Burgers’ equation

breakdown, 237

dependence on initial data, 241

Liouville’s theorem, 238

method of characteristics, 237

time of nonlinear interaction, 303

Cauchy problem, xiv

fully nonlinear scalar, 206–214

linear, 43–90

nonlinear, 215–257

quasilinear, 230–242

small data, 242–246

subcritical, 246–257

characteristic curves, 2, 13

and breakdown, 237–238

and finite speed, 58–59

fully nonlinear scalar, 206–214

method of, 2–16

359