scholarly journals Global existence and uniqueness of solutions to the three-dimensional Boussinesq equations

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Xin Liu
Keyword(s):  
Global Existence ◽  
Existence And Uniqueness ◽  
Three Dimensional ◽  
Boussinesq Equations ◽  
Uniqueness Of Solutions ◽  
Global Existence And Uniqueness

scholarly journals Existence and Uniqueness of Solutions for a Type of Generalized Zakharov System

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Rui Li ◽  
Xing Lin ◽  
Zongwei Ma ◽  
Jingjun Zhang
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Energy Conservation ◽  
Classical Solution ◽  
Sobolev Spaces ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Zakharov System ◽  
The Cauchy Problem ◽  
Global Existence And Uniqueness

We study the Cauchy problem for a type of generalized Zakharov system. With the help of energy conservation and approximate argument, we obtain global existence and uniqueness in Sobolev spaces for this system. Particularly, this result implies the existence of classical solution for this generalized Zakharov system.

Existence and uniqueness of discontinuous solutions for a hyperbolic system

1997 ◽  
Vol 127 (6) ◽  
pp. 1193-1205 ◽  
Author(s):  
Feimin Huang
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Hyperbolic System ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Discontinuous Solutions ◽  
The Cauchy Problem ◽  
Global Existence And Uniqueness

In this paper, we prove the global existence and uniqueness of solutions to the Cauchy problem of a hyperbolic system, which probably contains so-called δ-waves.

scholarly journals A necessary and sufficient condition for exponentially bounded existence and uniqueness

1973 ◽  
Vol 8 (1) ◽  
pp. 133-135 ◽  
Author(s):  
David Lowell Lovelady
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Global Existence ◽  
Existence And Uniqueness ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Uniqueness Of Solutions ◽  
Global Existence And Uniqueness ◽  
Necessary And Sufficient

A condition which was previously found to be sufficient for global existence and uniqueness of solutions of an ordinary differential equation is shown herein to be necessary, if it is also required that solutions are exponentially bounded.

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