We study the L^(2)-supercritical nonlinear Schrodinger equation(NLS) with a partial confinement,which is the limit case of the cigar-shaped model in Bose-Einstein condensate(BEC). By constructing a cross constrained v...We study the L^(2)-supercritical nonlinear Schrodinger equation(NLS) with a partial confinement,which is the limit case of the cigar-shaped model in Bose-Einstein condensate(BEC). By constructing a cross constrained variational problem and establishing the invariant manifolds of the evolution fow, we show a sharp condition for global existence.展开更多
In this paper, we present a cross-constrained variational method to study the Cauchy problem of the nonlinear Klein-Gordon equations with critical nonlinearity in two space dimensions. By constructing a type of cross-...In this paper, we present a cross-constrained variational method to study the Cauchy problem of the nonlinear Klein-Gordon equations with critical nonlinearity in two space dimensions. By constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow, we establish a sharp threshold of global existence and blowup of it. Furthermore, we answer the question： How small are the initial data if the solution exists globally.展开更多
This paper discusses nonlinear SchrSdinger equation with a harmonic potential. By constructing a different cross-constrained variational problem and the so-called invariant sets, we derive a new threshold for blow-up ...This paper discusses nonlinear SchrSdinger equation with a harmonic potential. By constructing a different cross-constrained variational problem and the so-called invariant sets, we derive a new threshold for blow-up and global existence of solutions.展开更多
基金supported by the National Natural Science Foundation of China(No.11871138)。
文摘We study the L^(2)-supercritical nonlinear Schrodinger equation(NLS) with a partial confinement,which is the limit case of the cigar-shaped model in Bose-Einstein condensate(BEC). By constructing a cross constrained variational problem and establishing the invariant manifolds of the evolution fow, we show a sharp condition for global existence.
基金Supported by the National Natural Science Foundation of China(No.10771151,10801102,10726034)Sichuan Youth Sciences and Technology Foundation(07ZQ026-009)China Postdoctoral Science Foundation Funded Project.
文摘In this paper, we present a cross-constrained variational method to study the Cauchy problem of the nonlinear Klein-Gordon equations with critical nonlinearity in two space dimensions. By constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow, we establish a sharp threshold of global existence and blowup of it. Furthermore, we answer the question： How small are the initial data if the solution exists globally.
基金Supported by the National Natural Science Foundation of China （No. 10747148, No. 10771151） and the Scientific Research Fund of Sichuan Provinciul Education Department （08ZA041）
文摘This paper discusses nonlinear SchrSdinger equation with a harmonic potential. By constructing a different cross-constrained variational problem and the so-called invariant sets, we derive a new threshold for blow-up and global existence of solutions.
