Geodesic
Strichartz Type Estimates for Oscillatory Problems for Semilinear Wave Equation
Serdica Mathematical Journal, Tome 26 (2000) no. 2, pp. 127-144.

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We treat the oscillatory problem for semilinear wave equation. The oscillatory initial data are of the type u(0, x) = h(x) + ε^(σ+1) * e^(il(x)/ε) * b0 (ε, x) ∂t u(0, x) = ε^σ * e^(il(x)/ε) * b1(ε, x). By using suitable variants of Strichartz estimate we extend the results from [6] on a priori estimates of the approximations of geometric optics.The main improvement is the fact that we can obtain a priori estimates for the case σ = 1, while in [6] we could treat only the case σ > n/2 − 1.
Keywords: Semilinear Wave Equation, Strichartz Estimate 
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     author = {Di Pomponio, Stefania},
     title = {Strichartz {Type} {Estimates} for {Oscillatory} {Problems} for {Semilinear} {Wave} {Equation}},
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Di Pomponio, Stefania. Strichartz Type Estimates for Oscillatory Problems for Semilinear Wave Equation. Serdica Mathematical Journal, Tome 26 (2000) no. 2, pp. 127-144. http://geodesic.mathdoc.fr/item/SMJ2_2000_26_2_a3/