The primary goal of this paper is to present a comprehensive study of the nonlinear Schrodinger equations with combined nonlinearities of the power-type and Hartreetype. Under certain structural conditions, the author...The primary goal of this paper is to present a comprehensive study of the nonlinear Schrodinger equations with combined nonlinearities of the power-type and Hartreetype. Under certain structural conditions, the authors are able to provide a complete picture of how the nonlinear Schrodinger equations with combined nonlinearities interact in the given energy space. The method used in the paper is based upon the Morawetz estimates and perturbation principles.展开更多
This paper is concerned with the decay estimate of high-order energy for a class of special time-dependent structural damped systems represented by Fourier multipliers. This model is widely used in the fields of semic...This paper is concerned with the decay estimate of high-order energy for a class of special time-dependent structural damped systems represented by Fourier multipliers. This model is widely used in the fields of semiconductivity, superconductivity, electromagnetic waves, electrolyte and electrode materials, etc.展开更多
The authors consider the scattering phenomena of the defocusing H^s-critical NLS.It is shown that if a solution of the defocusing NLS remains bounded in the critical homogeneous Sobolev norm on its maximal interval of...The authors consider the scattering phenomena of the defocusing H^s-critical NLS.It is shown that if a solution of the defocusing NLS remains bounded in the critical homogeneous Sobolev norm on its maximal interval of existence,then the solution is global and scatters.展开更多
The authors investigate the influence of a harmonic potential and random perturbations on the nonlinear Schr6dinger equations. The local and global well-posedness are proved with values in the space ∑（R^n）={f E HI...The authors investigate the influence of a harmonic potential and random perturbations on the nonlinear Schr6dinger equations. The local and global well-posedness are proved with values in the space ∑（R^n）={f E HI（R^n）, ｜·｜f ∈ L^2（R^n）}. When the nonlinearity is focusing and L2-supercritical, the authors give sufficient conditions for the solutions to blow up in finite time for both confining and repulsive potential. Especially for the repulsive case, the solution to the deterministic equation with the initial data satisfying the stochastic blow-up condition will also blow up in finite time. Thus, compared with the deterministic equation for the repulsive case, the blow-up condition is stronger on average, and depends on the regularity of the noise. If φ = 0, our results coincide with the ones for the deterministic equation.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.10871175,10931007)the Zhejiang Provincial Natural Science Foundation of China(No.Z6100217)
文摘The primary goal of this paper is to present a comprehensive study of the nonlinear Schrodinger equations with combined nonlinearities of the power-type and Hartreetype. Under certain structural conditions, the authors are able to provide a complete picture of how the nonlinear Schrodinger equations with combined nonlinearities interact in the given energy space. The method used in the paper is based upon the Morawetz estimates and perturbation principles.
基金supported by the National Natural Science Foundation of China (No.10871175)
文摘This paper is concerned with the decay estimate of high-order energy for a class of special time-dependent structural damped systems represented by Fourier multipliers. This model is widely used in the fields of semiconductivity, superconductivity, electromagnetic waves, electrolyte and electrode materials, etc.
基金supported by the National Natural Science Foundation of China(Nos.10931007,11226184,11271322)the Zhejiang Provincial Natural Science Foundation of China(No.Z6100217)
文摘The authors consider the scattering phenomena of the defocusing H^s-critical NLS.It is shown that if a solution of the defocusing NLS remains bounded in the critical homogeneous Sobolev norm on its maximal interval of existence,then the solution is global and scatters.
基金supported by the National Natural Science Foundation of China (Nos. 10871175,10931007,10901137)the Zhejiang Provincial Natural Science Foundation of China (No. Z6100217)the Specialized ResearchFund for the Doctoral Program of Higher Education (No. 20090101120005)
文摘The authors investigate the influence of a harmonic potential and random perturbations on the nonlinear Schr6dinger equations. The local and global well-posedness are proved with values in the space ∑（R^n）={f E HI（R^n）, ｜·｜f ∈ L^2（R^n）}. When the nonlinearity is focusing and L2-supercritical, the authors give sufficient conditions for the solutions to blow up in finite time for both confining and repulsive potential. Especially for the repulsive case, the solution to the deterministic equation with the initial data satisfying the stochastic blow-up condition will also blow up in finite time. Thus, compared with the deterministic equation for the repulsive case, the blow-up condition is stronger on average, and depends on the regularity of the noise. If φ = 0, our results coincide with the ones for the deterministic equation.
