Energy equality and uniqueness of weak solutions to MHD equations in L∞(0,T;Ln(Ω))

• Published in: Acta mathematica Sinica. English series Vol. 25; no. 5; pp. 803 - 814
• Main Authors: Yong, Yan, Jiu, Quan Sen
• Format: Journal Article
• Language: English
• Published: Heidelberg Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.05.2009; Springer Nature B.V
• Subjects: Energy; Equality; Mathematical analysis; Mathematics; Mathematics and Statistics; Navier-Stokes equations; Studies; Velocity; MHD equations; uniqueness; 35Q35; 76B03; energy equality; 35Q99; weak solutions

In this paper, we study the energy equality and the uniqueness of weak solutions to the MHD equations in the critical space L ∞ (0, T ; L n (Ω)). We prove that if the velocity u belongs to the critical space L ∞ (0, T ; L n (Ω)), the energy equality holds. On the basis of the energy equality, we fur...