On the global well-posedness for the nonlinear Schrödinger equations with large initial data of infinite L2L2 norm

It is shown that the Cauchy problem for the nonlinear Schrödinger equations iut+△u±|u|p−1u=0,x∈Rd,t>0 is globally well-posed for a class of initial data which lie in a LqLq space with qq near 2 when 1