本篇論文一開始會先介紹波方程和薛丁格方程上的Strichartz estimate，接著
會運用此估計，去解決波方程上的局部適定性問題(Local well-posedness)。

In this dissertation we discuss the Strichartz estimates on the Schrödinger
equation, Wave equation and application of the Wave equation.
First part we introduce some de…nitions, notations and basic theorems
from real analysis.
Second part we will prove the Strichartz estimates on the Schrödinger
equation follows from Tao’s Nonlinear dispersive equations: local and global
analysis and the Wave equation on R3. On the Wave equation, we will follow
the proofs from Christopher D. Sogge, Lectures on nonlinear wave equations.
The Littlewood-paley theorem plays a important role in this proof and we
use many technique of scaling.
Finally, we will use the Strichartz estimates on theWave equation of form
u = juj2u;Dom(u) = R1+3
+ with initial data u(0; ) = f; @tu(0; ) = g to
solve the existence of (weak) solutions and use same idea to get the local
well-posedness.

References
[1] Terence Tao, Nonlinear dispersive equations: local and global analysis,
2006.
[2] Christopher D. Sogge, Lectures on nonlinear wave equations, International
Press, 1995.
[3] Arick Shao, The Christ-Kiselev lemma.
[4] Gustavo Ponce, Felipe Linares, Introduction to nonlinear dispersive equa-
tions, Springer New York, 2009.
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