TY - JOUR
T1 - Global solutions for the Navier-Stokes equations in the rotational framework
AU - Iwabuchi, Tsukasa
AU - Takada, Ryo
N1 - Funding Information:
The authors would like to express his great thanks to Professor Hideo Kozono for his valuable advices and continuous encouragement. The authors would like to thank the referee for his constructive suggestions. The second author is partly supported by Research Fellow of the Japan Society for the Promotion of Science for Young Scientists.
PY - 2013/10
Y1 - 2013/10
N2 - The existence of global unique solutions to the Navier-Stokes equations with the Coriolis force is established in the homogeneous Sobolev spaces Hs (ℝ3)3 for 1/2 < s < 3/4 if the speed of rotation is sufficiently large. This phenomenon is so-called the global regularity. The relationship between the size of initial datum and the speed of rotation is also derived. The proof is based on the space time estimates of the Strichartz type for the semigroup associated with the linearized equations. In the scaling critical space H1/2(ℝ3)3, the global regularity is also shown.
AB - The existence of global unique solutions to the Navier-Stokes equations with the Coriolis force is established in the homogeneous Sobolev spaces Hs (ℝ3)3 for 1/2 < s < 3/4 if the speed of rotation is sufficiently large. This phenomenon is so-called the global regularity. The relationship between the size of initial datum and the speed of rotation is also derived. The proof is based on the space time estimates of the Strichartz type for the semigroup associated with the linearized equations. In the scaling critical space H1/2(ℝ3)3, the global regularity is also shown.
UR - https://www.scopus.com/pages/publications/84883765122
UR - https://www.scopus.com/pages/publications/84883765122#tab=citedBy
U2 - 10.1007/s00208-013-0923-4
DO - 10.1007/s00208-013-0923-4
M3 - Article
AN - SCOPUS:84883765122
SN - 0025-5831
VL - 357
SP - 727
EP - 741
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 2
ER -