TY - JOUR
T1 - Asymptotic stability for the Navier-Stokes equations
AU - Fan, Jishan
AU - Ozawa, Tohru
N1 - Funding Information:
Mathematics Subject Classifications (2000): 76N15, 35Q30, 35Q35, 35M20 Key words: Asymptotic stability, Navier-Stokes equations, Besov spaces. ∗Supported by NSFC (Grant No. 10301014).
PY - 2008/5
Y1 - 2008/5
N2 - We prove the asymptotic stability for weak solutions to the 3-D Navier-Stokes equations in the class ∇u ∈ L1(0, ∞; Ḃ∞∞0(ℝ3)) ∩ LLogL(0, ∞; Ḃ∞∞0(ℝ3)) with arbitrary initial and external perturbations. This solves a problem due to Yong Zhou (Proc. Roy. Soc. Edinburgh, 136A (2006), 1099-1109).
AB - We prove the asymptotic stability for weak solutions to the 3-D Navier-Stokes equations in the class ∇u ∈ L1(0, ∞; Ḃ∞∞0(ℝ3)) ∩ LLogL(0, ∞; Ḃ∞∞0(ℝ3)) with arbitrary initial and external perturbations. This solves a problem due to Yong Zhou (Proc. Roy. Soc. Edinburgh, 136A (2006), 1099-1109).
KW - Asymptotic stability
KW - Besov spaces
KW - Navier-Stokes equations
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U2 - 10.1007/s00028-008-0396-1
DO - 10.1007/s00028-008-0396-1
M3 - Article
AN - SCOPUS:44549085560
SN - 1424-3199
VL - 8
SP - 379
EP - 389
JO - Journal of Evolution Equations
JF - Journal of Evolution Equations
IS - 2
ER -