Nonlinear Wave Equations

  title={Nonlinear Wave Equations},
  author={Christopher W. Curtis and Anton Dzhamay and Willy A. Hereman and Barbara Prinari},
where := −∂2 t +∆ and u[0] := (u, ut)|t=0. The equation is semi-linear if F is a function only of u, (i.e. F = F (u)), and quasi-linear if F is also a function of the derivatives of u (i.e. F = F (u,Du), where D := (∂t,∇)). The goal is to use energy methods to prove local well-posedness for quasilinear equations with data (f, g) ∈ Hs × Hs−1 for large enough s, and then to derive Strichartz estimates to deal with semi-linear problems with data (f, g) ∈ Ḣ1 × L2. We begin, however, by deriving… 

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