The global solution of initial value problem for nonlinear Schrödinger-Boussinesq equation in 3-dimensions

1990 ◽  
Vol 6 (1) ◽  
pp. 11-21 ◽  
Author(s):  
Boling Guo ◽  
Longjun Shen
Keyword(s):  
Global Solution ◽  
Initial Value Problem ◽  
Boussinesq Equation ◽  
Initial Value ◽  
Nonlinear Schrödinger

Optimal L 2 -decay of solutions to a cubic dissipative nonlinear Schrödinger equation

2021 ◽  
pp. 1-13
Author(s):  
Kita Naoyasu ◽  
Sato Takuya
Keyword(s):  
Sobolev Space ◽  
Global Solution ◽  
Initial Value Problem ◽  
Trivial Solution ◽  
Decay Estimate ◽  
Weighted Sobolev Space ◽  
The Other ◽  
Initial Value ◽  
Decay Of Solutions ◽  
Dissipative Nonlinearity

This paper presents the optimality of decay estimate of solutions to the initial value problem of 1D Schrödinger equations containing a long-range dissipative nonlinearity, i.e., λ | u | 2 u. Our aim is to obtain the two results. One asserts that, if the L 2 -norm of a global solution, with an initial datum in the weighted Sobolev space, decays at the rate more rapid than ( log t ) − 1 / 2 , then it must be a trivial solution. The other asserts that there exists a solution decaying just at the rate of ( log t ) − 1 / 2 in L 2 .

L∞C(ℝn)-decay of classical solutions for nonlinear Schrödinger equations

1986 ◽  
Vol 104 (3-4) ◽  
pp. 309-327 ◽  
Author(s):  
Nakao Hayashi ◽  
Masayoshi Tsutsumi
Keyword(s):  
Schrödinger Equation ◽  
Initial Value Problem ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Classical Solutions ◽  
Initial Value ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Sign Conditions ◽  
Image Position

SynopsisWe study the initial value problem for the nonlinear Schrödinger equationUnder suitable regularity assumptions on f and ø and growth and sign conditions on f, it is shown that the maximum norms of solutions to (*) decay as t→² ∞ at the same rate as that of solutions to the free Schrödinger equation.

Decay of solutions to a two-layer quasi-geostrophic model

2017 ◽  
Vol 15 (04) ◽  
pp. 595-606 ◽  
Author(s):  
Boling Guo ◽  
Daiwen Huang ◽  
Jingjun Zhang
Keyword(s):  
Fluid Dynamics ◽  
Galerkin Method ◽  
Decay Rate ◽  
Global Solution ◽  
Initial Value Problem ◽  
Splitting Method ◽  
Geophysical Fluid Dynamics ◽  
Initial Value ◽  
Decay Of Solutions

We consider a two-layer quasi-geostrophic model in geophysical fluid dynamics. By Faedo–Galerkin method and asymptotic argument, we prove the existence of the global solution to the initial value problem of this model in [Formula: see text]. Moreover, using the Fourier splitting method, we also obtain the decay rate of the solutions.

An iteration method for a nonlinear differential equation describing the convergence to equilibrium in a system of reacting polymers

1981 ◽  
Vol 375 (1763) ◽  
pp. 529-542
Keyword(s):  
Differential Equation ◽  
Initial Data ◽  
Global Solution ◽  
Nonlinear Differential Equation ◽  
Initial Value Problem ◽  
Iteration Method ◽  
Constructive Method ◽  
Convergence To Equilibrium ◽  
Initial Value

A constructive method is presented to give the global solution to a nonlinear initial value problem describing the convergence to equilibrium in a system of reacting polymers. The solution is proved to be unique and continuous with respect to small variations in the initial data.

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