Abstract
We consider the uniqueness of bounded continuous L3, ∞-solutions on the whole time axis to the Navier-Stokes equations in 3-dimensional unbounded domains. Here, Lp, q denotes the scale of Lorentz spaces. Thus far, uniqueness of such solutions to the Navier-Stokes equations in unbounded domain, roughly speaking, is known only for a small solution in BC(ℝ; L3, ∞) within the class of solutions which have sufficiently small L∞(L3, ∞)-norm. In this paper, we discuss another type of uniqueness theorem for solutions in BC(ℝ; L3, ∞) using a smallness condition for one solution and a precompact range condition for the other one. The proof is based on the method of dual equations.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
