Global Existence Of Solutions To A Class Of Quasilinear Wave Equation

In this thesis we mainly investigate such a Cauchy problem It is shown that this equation has a global solution for all t≥0if the initial datas are sufficiently small. We will apply for the approach that deals with the problem together wit in the literature [11]. To this end, it suffices to derive the sharp decay estimates of solution for lower order derivatives by expressing the metric and the wave operator in the null frame,using the weak decay estimates to control the angular derivatives, and integrating along characteristics. From this, the energy estimates for higher order derivatives can be obtained. Finally, by the continuity argument we obtain the weak decay estimates of solution and show the global existence.