A Regularity Criterion in Weak Spaces to Boussinesq Equations

• Main Authors: Ravi P. Agarwal, Sadek Gala, Maria Alessandra Ragusa
• Format: Article
• Language: English
• Published: MDPI AG 2020-06-01
• Series: Mathematics
• Subjects: Regularity results; Cauchy problem; Boussinesq equations; Lorentz spaces; Navier-Stokes equations; MHD equations
• Online Access: https://www.mdpi.com/2227-7390/8/6/920
• ISSN: 2227-7390

In this paper, we study the regularity of weak solutions to the incompressible Boussinesq equations in <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi mathvariant="double-struck">R</mi> <mn>3</mn> </msup> <mo>×</mo> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mi>T</mi> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula>. The main goal is to establish the regularity criterion in terms of one velocity component and the gradient of temperature in Lorentz spaces.