Funkcialaj Ekvacioj
Print ISSN : 0532-8721
Uniqueness of Steady Navier-Stokes Flows in Exterior Domains
Tomoyuki Nakatsuka
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2013 Volume 56 Issue 2 Pages 323-337

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Abstract

We consider the uniqueness of stationary solutions to the Navier-Stokes equation in 3-dimensional exterior domains within the class uL3, ∞ with ∇uL3/2, ∞, where L3, ∞ and L3/2, ∞ are the Lorentz spaces. It is shown that if solutions u and v satisfy the conditions that u is small in L3, ∞ and vL3 + L, then u = v. The proof relies upon the regularity theory for the perturbed Stokes equation.

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© 2013 by the Division of Functional Equations, The Mathematical Society of Japan
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