Linear Profile decomposition of three-dimensional Schr?dinger equations
In order to study the defect of compactness problem of the Strichartz estimates for the solution of the linear Schrödinger equations,for the bounded solution vector sequences of the three-dimensional linear Schrödinger equations in H1(R3)× H1(R3),the profile decomposition method of the solution sequences was used to construct a(1/√hn)U((t-tn)/h2n,(x-xn)/hn)-type Profile decomposition sum of the solu-tion vector subsequences.Among them,U is the solution vector of the linear Schrödinger equations,with a small remainder under the estimate of the Strichartz norm.Firstly,the sequence family of stretching trans-formation parameters was determined,and the Profile decomposition family was determined using the ideas of Fourier transform and iteration.Secondly,the convergence of the Profile decomposition sum was verified,the convergence of the remainder under the Strichartz norm was demonstrated.Finally,it was proved that when the solution sequences of the linear Schrödinger equations are bounded,it can be decomposed into a form of the sum of the solution vector subsequences.
万方数据
维普
