Global Strong Solutions to Cauchy Problem of 1D Non-resistive MHD Equations with No Vacuum at Infinity

2021 ◽  
Vol 175 (1) ◽  
Author(s):  
Xiaolian Ai ◽  
Zilai Li ◽  
Yulin Ye
Keyword(s):  
Cauchy Problem ◽  
Strong Solutions ◽  
Mhd Equations ◽  
Global Strong Solutions

scholarly journals On non-resistive limit of 1D MHD equations with no vacuum at infinity

2021 ◽  
Vol 11 (1) ◽  
pp. 702-725
Author(s):  
Zilai Li ◽  
Huaqiao Wang ◽  
Yulin Ye
Keyword(s):  
Cauchy Problem ◽  
A Priori ◽  
Strong Solutions ◽  
Mhd Equations ◽  
Well Posedness ◽  
Large Initial Data ◽  
One Dimensional ◽  
The Cauchy Problem ◽  
Global Strong Solutions ◽  
The One

Abstract In this paper, the Cauchy problem for the one-dimensional compressible isentropic magnetohydrodynamic (MHD) equations with no vacuum at infinity is considered, but the initial vacuum can be permitted inside the region. By deriving a priori ν (resistivity coefficient)-independent estimates, we establish the non-resistive limit of the global strong solutions with large initial data. Moreover, as a by-product, the global well-posedness of strong solutions for the compressible resistive MHD equations is also established.

scholarly journals The Cauchy problem of a two-phase flow model for a mixture of non-interacting compressible fluids

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Zhen Cheng ◽  
Wenjun Wang
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Strong Solutions ◽  
Compressible Fluids ◽  
Existence Theory ◽  
Optimal Time ◽  
Two Phase ◽  
Frequency Decomposition ◽  
The Cauchy Problem ◽  
Global Strong Solutions

<p style='text-indent:20px;'>In this paper, we consider the global existence of the Cauchy problem for a version of one velocity Baer-Nunziato model with dissipation for the mixture of two compressible fluids in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^3 $\end{document}</tex-math></inline-formula>. We get the existence theory of global strong solutions by using the decaying properties of the solutions. The energy method combined with the low-high-frequency decomposition is used to derive such properties and hence the global existence. As a byproduct, the optimal time decay estimates of all-order spatial derivatives of the pressure and the velocity are obtained.</p>

scholarly journals Large Time Existence of Special Strong Solutions to MHD Equations in Cylindrical Domains

2017 ◽  
Vol 20 (3) ◽  
pp. 1013-1034
Author(s):  
Bernard Nowakowski ◽  
Gerhard Ströhmer ◽  
Wojciech M. Zaja̧czkowski
Keyword(s):  
Large Time ◽  
Strong Solutions ◽  
Mhd Equations ◽  
Cylindrical Domains ◽  
Time Existence

scholarly journals Global existence of strong solutions for incompressible hydrodynamic flow of liquid crystals with vacuum

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1247-1257 ◽  
Author(s):  
Shijin Ding ◽  
Jinrui Huang ◽  
Fengguang Xia
Keyword(s):  
Cauchy Problem ◽  
Liquid Crystals ◽  
Global Existence ◽  
Existence And Uniqueness ◽  
Strong Solutions ◽  
Hydrodynamic Flow ◽  
Three Dimensions ◽  
Small Initial Data ◽  
The Cauchy Problem ◽  
Global Existence And Uniqueness

We consider the Cauchy problem for incompressible hydrodynamic flow of nematic liquid crystals in three dimensions. We prove the global existence and uniqueness of the strong solutions with nonnegative p0 and small initial data.

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