Differential and Integral Equations

Generalized Strichartz estimates on perturbed wave equation and applications on Strauss conjecture

Xin Yu

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Abstract

In this paper we prove a general Strichartz estimate for certain perturbed wave equations, and here we can drop the nontrapping hypothesis and handle trapping obstacles with some loss of derivatives for data in the local energy decay estimates. We then give the obstacle version of the sharp life span for semilinear wave equations when $n=3,p<p_c$, by using the real interpolation method, and by getting corresponding finite time Strichartz estimates (see Section 3). Finally, as another application, we get the Strauss conjecture for semilinear wave equations with several convex obstacles when $n=3,4$ (see Section 4).

Article information

Source
Differential Integral Equations, Volume 24, Number 5/6 (2011), 443-468.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356018913

Mathematical Reviews number (MathSciNet)
MR2809616

Zentralblatt MATH identifier
1249.35224

Subjects
Primary: 35L05: Wave equation 35B20: Perturbations 35B65: Smoothness and regularity of solutions 35B33: Critical exponents

Citation

Yu, Xin. Generalized Strichartz estimates on perturbed wave equation &#13;and applications on Strauss conjecture. Differential Integral Equations 24 (2011), no. 5/6, 443--468. https://projecteuclid.org/euclid.die/1356018913


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