On the global existence and small dissipation limit for generalized dissipative Zakharov system

2018 ◽  
Vol 41 (10) ◽  
pp. 3718-3749 ◽  
Author(s):  
Xueqin Wang ◽  
Yadong Shang
Keyword(s):  
Global Existence ◽  
Zakharov System ◽  
Small Dissipation

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.

scholarly journals L2-CONCENTRATION PHENOMENON FOR ZAKHAROV SYSTEM BELOW ENERGY NORM

2009 ◽  
Vol 11 (01) ◽  
pp. 27-57 ◽  
Author(s):  
DAOYUAN FANG ◽  
SIJIA ZHONG
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Existence Result ◽  
Space Dimension ◽  
Blow Up ◽  
Energy Norm ◽  
Zakharov System ◽  
Concentration Result ◽  
Global Existence Result ◽  
Concentration Phenomenon

In this paper, we prove an L2-concentration result of Zakharov system in space dimension two, with radial initial data [Formula: see text], when blow up of the solution happens by I-method. In addition to that, we find a blow up character of this system. Furthermore, we improve the global existence result of Bourgain's to the above-mentioned spaces.

Remarks on nonlinear elastic waves with null conditions

2020 ◽  
Vol 26 ◽  
pp. 121
Author(s):  
Dongbing Zha ◽  
Weimin Peng
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Elastic Waves ◽  
Wave Equations ◽  
Alternative Proof ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Hyperelastic Materials ◽  
Variational Structure ◽  
Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

The Affective Politics of Karma among Buddhist Cancer Charities in Vietnam

2020 ◽  
Vol 15 (4) ◽  
pp. 33-62
Author(s):  
Sara Swenson
Keyword(s):  
Public Health ◽  
Global Existence ◽  
Food Production ◽  
Public Health Intervention ◽  
Health Intervention ◽  
Moral Failure ◽  
Cancer Rates ◽  
Charity Work

In this article, I explore how Buddhist charity workers in Vietnam interpret rising cancer rates through understandings of karma. Rather than framing cancer as a primarily physical or medical phenomenon, volunteers state that cancer is a product of collective moral failure. Corruption in public food production is both caused by and perpetuates bad karma, which negatively impacts global existence. Conversely, charity work creates merit, which can improve collective karma and benefit all living beings. I argue that through such interpretations of karma, Buddhist volunteers understand their charity at cancer hospitals as an affective and ethical form of public health intervention.

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