On the Nonlinear Schrödinger Equation

2xt² Cauchy problem Chadam Chapter const const(1 const(1+t decay estimates Doctor of Philosophy Don Weingarten energy conservation existence of solutions finite function ƒª gamma function Ginibre and Velo Ginibre-Velo's global existence global solution Hence Hölder's inequality Indiana University integrable integrand interpolation interval itHo Ju² Ju²1 Jul2 L2-norm let u(t Let u(x,t Lipschitz property llull lu(t lul² Math Mathematical Physics N₁ non-local Coulomb Non-local Nonlinearities nonlinear Schrödinger equation nonlinear term norm np² p+1 p+1 perturbation Power Nonlinearities proof of Lemma pseudo-conformal conservation law Pseudo-Conformal Invariant q-norms real-valued S-valued solution scattering occurs scattering solution Scattering Theory Schrödinger equation 1.1 Segal's Shigemitsu Kadekawa Sobolev inequality solution in H¹(R solution of 1.2 solution of equation space dimensions Strauss technical Lemma 4.5 tion u1² dx ul² Yukawa potential Δυ