Orlicz Regularity for Non-Divergence Parabolic Systems with Partially Vmo Coefficients

2015 ◽  
Vol 116 (1) ◽  
pp. 141
Author(s):  
Maochun Zhu ◽  
Pengcheng Niu ◽  
Xiaojing Feng
Keyword(s):  
Strong Solutions ◽  
Parabolic Systems ◽  
Spatial Variables ◽  
Vmo Coefficients

This work treats the interior Orlicz regularity for strong solutions of a class of non-divergence parabolic systems with coefficients just measurable in time and VMO in the spatial variables.

scholarly journals $L^\infty$-estimates for parabolic systems with VMO-coefficients

2010 ◽  
Vol 3 (2) ◽  
pp. 299-309 ◽  
Author(s):  
Horst Heck ◽  
◽  
Matthias Hieber ◽  
Kyriakos Stavrakidis
Keyword(s):  
Parabolic Systems ◽  
Vmo Coefficients

Regularity in Morrey Spaces of Strong Solutions to Nondivergence Elliptic Equations with VMO Coefficients

1998 ◽  
Vol 5 (5) ◽  
pp. 425-440
Author(s):  
Dashan Fan ◽  
Shanzhen Lu ◽  
Dachun Yang
Keyword(s):  
Elliptic Equations ◽  
Singular Integrals ◽  
Strong Solutions ◽  
Morrey Spaces ◽  
Vmo Coefficients

Abstract In this paper, by means of the theories of singular integrals and linear commutators, the authors establish the regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients.

Large-time behavior of strong solutions to the compressible magnetohydrodynamic system in the critical framework

2018 ◽  
Vol 15 (02) ◽  
pp. 259-290 ◽  
Author(s):  
Weixuan Shi ◽  
Jiang Xu
Keyword(s):  
Large Time ◽  
Characteristic Root ◽  
Global Solutions ◽  
Strong Solutions ◽  
Parabolic Systems ◽  
Large Time Behavior ◽  
Optimal Time ◽  
Asymptotic Behavior Of Solutions ◽  
Time Behavior ◽  
Mhd System

We study the compressible viscous magnetohydrodynamic (MHD) system and investigate the large-time behavior of strong solutions near constant equilibrium (away from vacuum). In the 80s, Umeda et al. considered the dissipative mechanisms for a rather general class of symmetric hyperbolic–parabolic systems, which is given by [Formula: see text] Here, [Formula: see text] denotes the characteristic root of linearized equations. From the point of view of dissipativity, Kawashima in his doctoral dissertation established the optimal time-decay estimates of [Formula: see text]-[Formula: see text]) type for solutions to the MHD system. Now, by using Fourier analysis techniques, we present more precise description for the large-time asymptotic behavior of solutions, not only in extra Lebesgue spaces but also in a full family of Besov norms with the negative regularity index. Precisely, we show that the [Formula: see text] norm (the slightly stronger [Formula: see text] norm in fact) of global solutions with the critical regularity, decays like [Formula: see text] as [Formula: see text]. Our decay results hold in case of large highly oscillating initial velocity and magnetic fields, which improve Kawashima’s classical efforts.

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