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

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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 -