scholarly journals The Cauchy Problem for the Euler–Poisson System and Derivation of the Zakharov–Kuznetsov Equation

2013 ◽  
pp. 181-213 ◽  
Author(s):  
David Lannes ◽  
Felipe Linares ◽  
Jean-Claude Saut
Keyword(s):  
Cauchy Problem ◽  
Poisson System ◽  
The Cauchy Problem

scholarly journals The Cauchy Problem for the 3-D Vlasov–Poisson System with Point Charges

2011 ◽  
Vol 201 (1) ◽  
pp. 1-26 ◽  
Author(s):  
Carlo Marchioro ◽  
Evelyne Miot ◽  
Mario Pulvirenti
Keyword(s):  
Cauchy Problem ◽  
Poisson System ◽  
The Cauchy Problem

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

Fundamental Serrin type regularity criteria for 3D MHD fluid passing through the porous medium

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1287-1293 ◽  
Author(s):  
Zujin Zhang ◽  
Dingxing Zhong ◽  
Shujing Gao ◽  
Shulin Qiu
Keyword(s):  
Cauchy Problem ◽  
Porous Medium ◽  
Regularity Criterion ◽  
Regularity Criteria ◽  
The Cauchy Problem ◽  
Appl Math

In this paper, we consider the Cauchy problem for the 3D MHD fluid passing through the porous medium, and provide some fundamental Serrin type regularity criteria involving the velocity or its gradient, the pressure or its gradient. This extends and improves [S. Rahman, Regularity criterion for 3D MHD fluid passing through the porous medium in terms of gradient pressure, J. Comput. Appl. Math., 270 (2014), 88-99].

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