scholarly journals Erratum: On the Cauchy problem for Yang–Mills equations with external current [J. Math. Phys. 30, 1699 (1989)]

1990 ◽  
Vol 31 (9) ◽  
pp. 2334-2334
Author(s):  
Z. Swierczynski
Keyword(s):  
Cauchy Problem ◽  
External Current ◽  
Yang Mills ◽  
The Cauchy Problem ◽  
Math Phys

scholarly journals A new blow-up criterion for the N – abc family of Camassa-Holm type equation with both dissipation and dispersion

2020 ◽  
Vol 18 (1) ◽  
pp. 194-203 ◽  
Author(s):  
Zaiyun Zhang ◽  
Limei Li ◽  
Chunhua Fang ◽  
Fan He ◽  
Chuangxia Huang ◽  
...  
Keyword(s):  
Cauchy Problem ◽  
Positive Solutions ◽  
Finite Time ◽  
Blow Up ◽  
Type Equation ◽  
Holm Equation ◽  
The Cauchy Problem ◽  
Math Phys ◽  
Blow Up Criterion

Abstract In this paper, we investigate the Cauchy problem for the N – abc family of Camassa-Holm type equation with both dissipation and dispersion. Furthermore, we establish the blow-up result of the positive solutions in finite time under certain conditions on the initial datum. This result complements the early one in the literature, such as [E. Novruzov, Blow-up phenomena for the weakly dissipative Dullin-Gottwald-Holm equation, J. Math. Phys. 54 (2013), no. 9, 092703, DOI 10.1063/1.4820786] and [Z.Y. Zhang, J.H. Huang, and M.B. Sun, Blow-up phenomena for the weakly dissipative Dullin-Gottwald-Holm equation revisited, J. Math. Phys. 56 (2015), no. 9, 092701, DOI 10.1063/1.4930198].

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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