scholarly journals A Regularity Criterion in Weak Spaces to Boussinesq Equations

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 920 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Sadek Gala ◽  
Maria Alessandra Ragusa
Keyword(s):  
Weak Solutions ◽  
Velocity Component ◽  
Boussinesq Equations ◽  
Regularity Criterion ◽  
Lorentz Spaces ◽  
Regularity Of Weak Solutions

In this paper, we study the regularity of weak solutions to the incompressible Boussinesq equations in R 3 × ( 0 , T ) . The main goal is to establish the regularity criterion in terms of one velocity component and the gradient of temperature in Lorentz spaces.

scholarly journals Regularity Criteria for the 3D Magneto-Hydrodynamics Equations in Anisotropic Lorentz Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 625
Author(s):  
Maria Alessandra Ragusa ◽  
Fan Wu
Keyword(s):  
Weak Solutions ◽  
Lorentz Space ◽  
Regularity Criterion ◽  
Lorentz Spaces ◽  
Mhd Equations ◽  
Regularity Criteria ◽  
Regularity Of Weak Solutions ◽  
Incompressible Mhd ◽  
Hydrodynamics Equations

In this paper, we investigate the regularity of weak solutions to the 3D incompressible MHD equations. We provide a regularity criterion for weak solutions involving any two groups functions (∂1u1,∂1b1), (∂2u2,∂2b2) and (∂3u3,∂3b3) in anisotropic Lorentz space.

scholarly journals Logarithmically Improved Regularity Criterion for the 3D Micropolar Fluid Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hui Zhang
Keyword(s):  
Besov Space ◽  
Strong Solution ◽  
Weak Solutions ◽  
Micropolar Fluid ◽  
Regularity Criterion ◽  
Vorticity Field ◽  
Regularity Of Weak Solutions ◽  
Fluid Equations ◽  
Incompressible Micropolar Fluid ◽  
Micropolar Fluid Equations

We study the regularity of weak solutions to the incompressible micropolar fluid equations. We obtain an improved regularity criterion in terms of vorticity of velocity in Besov space. It is proved that if the vorticity field satisfies ∫0T∇×uB˙∞,∞0/1+log1+∇×uB˙∞,∞0dt<∞ then the strong solution can be smoothly extended after time T.

scholarly journals A regularity criterion of weak solutions to the 3D Boussinesq equations

2017 ◽  
Vol 2 (3) ◽  
pp. 451-457 ◽  
Author(s):  
Ahmad Mohammed Alghamdi ◽  
◽  
Sadek Gala ◽  
Maria Alessandra Ragusa ◽  
◽  
...  
Keyword(s):  
Weak Solutions ◽  
Boussinesq Equations ◽  
Regularity Criterion
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