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 q Lx, 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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