scholarly journals GLOBAL WELL-POSEDNESS OF THE GENERALIZED ROTATING MAGNETOHYDRODYNAMICS EQUATIONS IN VARIABLE EXPONENT FOURIER-BESOV SPACES

2020 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Muhammad Zainul Abidin ◽  
◽  
Jiecheng Chen
Keyword(s):  
Besov Spaces ◽  
Variable Exponent ◽  
Well Posedness ◽  
Magnetohydrodynamics Equations

scholarly journals Global Well-Posedness and Analyticity of the Primitive Equations of Geophysics in Variable Exponent Fourier–Besov Spaces

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 165
Author(s):  
Muhammad Zainul Abidin ◽  
Naeem Ullah ◽  
Omer Abdalrhman Omer
Keyword(s):  
Cauchy Problem ◽  
Besov Spaces ◽  
Variable Exponent ◽  
Three Dimensional ◽  
Primitive Equations ◽  
Well Posedness ◽  
Small Initial Data ◽  
Fourier Localization ◽  
Gevrey Class Regularity ◽  
The Cauchy Problem

We consider the Cauchy problem of the three-dimensional primitive equations of geophysics. By using the Littlewood–Paley decomposition theory and Fourier localization technique, we prove the global well-posedness for the Cauchy problem with the Prandtl number P=1 in variable exponent Fourier–Besov spaces for small initial data in these spaces. In addition, we prove the Gevrey class regularity of the solution. For the primitive equations of geophysics, our results can be considered as a symmetry in variable exponent Fourier–Besov spaces.

Global well-posedness and self-similarity for semilinear wave equations in a time-weighted framework of Besov type

2020 ◽  
Vol 17 (01) ◽  
pp. 123-139
Author(s):  
Lucas C. F. Ferreira ◽  
Jhean E. Pérez-López
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Besov Spaces ◽  
Wave Equations ◽  
Well Posedness ◽  
Self Similarity ◽  
Semilinear Wave Equations ◽  
Semilinear Wave Equation

We show global-in-time well-posedness and self-similarity for the semilinear wave equation with nonlinearity [Formula: see text] in a time-weighted framework based on the larger family of homogeneous Besov spaces [Formula: see text] for [Formula: see text]. As a consequence, in some cases of the power [Formula: see text], we cover a initial-data class larger than in some previous results. Our approach relies on dispersive-type estimates and a suitable [Formula: see text]-product estimate in Besov spaces.

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