Abstract
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.