The work is devoted to establish the spacetime bound for the energy-critical nonlinear wave equation □u=u^(3/7) in R^(1+5) Then we build the explicit Strichartz bound ||u||_(L_t^(58/27) L_x^(29/6) (R^(1+5)))?C(1+CE)^CE^100 for some absolute C>0 by using the techniques of the mass and energy concentration and interval-comparing estimate from [21] And we reconsider the energy-critical nonlinear wave equation □u=u^(3) in R^(1+4) Thus we also build the explicit Strichartz bound ||u||_(L_t^(5/2) L_x^(20/3) (R^(1+4)))?C(1+CE)^CE^24 for some absolute C>0 by using the techniques of the energy outside tha big ball and the method of the interval-size comparing from [21]

Date of Award | 2018 Jan 23 |
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Original language | English |
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Supervisor | Hsi-Wei Shih (Supervisor) |
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The Strichartz norm control in the four and five dimensional energy-critical nonlinear wave equations

育嶙, 朱. (Author). 2018 Jan 23

Student thesis: Master's Thesis