TY - CHAP
T1 - Global existence results for the Navier–Stokes equations in the rotational framework in Fourier–Besov spaces
AU - Fang, Daoyuan
AU - Han, Bin
AU - Hieber, Matthias Georg
PY - 2015
Y1 - 2015
N2 - Consider the equations of Navier–Stokes in ℝ3 in the rotational setting, i.e., with Coriolis force. It is shown that this set of equations admits a unique, global mild solution provided the initial data is small with respect to the norm of the Fourier–Besov space ḞB2−3/p p,r (ℝ3), where p ∈ (1,∞] and r ∈ [1,∞]. In the two-dimensional setting, a unique, global mild solution to this set of equations exists for non-small initial data u0 ∈ Lp σ(ℝ2) for p ∈ [2,∞).
AB - Consider the equations of Navier–Stokes in ℝ3 in the rotational setting, i.e., with Coriolis force. It is shown that this set of equations admits a unique, global mild solution provided the initial data is small with respect to the norm of the Fourier–Besov space ḞB2−3/p p,r (ℝ3), where p ∈ (1,∞] and r ∈ [1,∞]. In the two-dimensional setting, a unique, global mild solution to this set of equations exists for non-small initial data u0 ∈ Lp σ(ℝ2) for p ∈ [2,∞).
KW - Global existence
KW - Navier–Stokes
KW - Rotational framework
UR - http://www.scopus.com/inward/record.url?scp=84958980774&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84958980774&partnerID=8YFLogxK
M3 - Chapter
AN - SCOPUS:84958980774
VL - 250
T3 - Operator Theory: Advances and Applications
SP - 199
EP - 211
BT - Operator Theory: Advances and Applications
PB - Springer International Publishing
ER -