Global existence of large solutions for the generalized Poisson–Nernst–Planck equations

2021 ◽  
Vol 498 (1) ◽  
pp. 124943
Author(s):  
Jihong Zhao
Keyword(s):  
Global Existence ◽  
Generalized Poisson ◽  
Large Solutions

scholarly journals Global large solutions to the planar magnetohydrodynamics equations with constant heat conductivity

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Wei Li ◽  
Zhaoyang Shang
Keyword(s):  
Global Existence ◽  
Heat Conductivity ◽  
Strong Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Constant Heat ◽  
Magnetic Diffusion ◽  
New Methods ◽  
Large Solutions ◽  
Initial Boundary Value

Abstract This paper is concerned with global existence of large solutions to the initial-boundary value problem of the planar magnetohydrodynamic compressible flow. Under the assumptions that viscosity and heat conductivity coefficients are constants, magnetic diffusion is a function of the specific volume, we obtain the global existence of strong solutions. Some new methods are developed to deal with the complex interaction between the hydrodynamic and magnetodynamics effects.

scholarly journals Global Existence and Temporal Decay of Large Solutions for the Poisson--Nernst--Planck Equations in Low Regularity Spaces

2021 ◽  
Author(s):  
Jihong Zhao ◽  
Xilan Liu
Keyword(s):  
Global Existence ◽  
Decay Rates ◽  
Large Solution ◽  
Low Regularity ◽  
Charged Species ◽  
Temporal Decay ◽  
Large Solutions ◽  
Optimal Decay Rates ◽  
Optimal Decay ◽  
Positively Charged

We are concerned with the global existence and decay rates of large solutions for the Poisson–Nernst–Planck equations. Based on careful observation of algebraic structure of the equations and using the weighted Chemin–Lerner type norm, we obtain the global existence and optimal decay rates of large solutions without requiring the summation of initial densities of a negatively and positively charged species is small enough. Moreover, the large solution is obtained for initial data belonging to the low regularity Besov spaces with different regularity and integral indices for the different charged species, which indicates more specific coupling relations between the negatively and positively charged species.

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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