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
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