Liouville type Theorems for the 3D stationary Hall‐MHD equations. Issue 5 (19th March 2020)

• Record Type: Journal Article
• Authors: Li, Zhouyu; Niu, Pengcheng
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 100:Issue 5(2020)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2020-03-19
• Subjects: Hall‐MHD system; liouville type theorem; lorentz space; navier‐Stokes system; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.201900200
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract: The purpose of this paper is to establish the Liouville type theorems for the stationary Hall‐MHD equations on R 3 . We prove that the velocity and magnetic fields, belonging to some Lorentz spaces, must be zero. In particular, we also show Liouville type results for 3D stationary Navier‐Stokes equations. Our results extend and generalize previous result contained in Kozono, et al., (2017) [15]. Abstract : The purpose of this paper is to establish the Liouville type theorems for the stationary Hall‐MHD equations on R 3 . We prove that the velocity and magnetic fields, belonging to some Lorentz spaces, must be zero. In particular, we also show Liouville type results for 3D stationary Navier‐Stokes equations. Our results extend and generalize previous result contained in Kozono, et al., (2017) [15].