Global existence results for the Navier-Stokes equations in the rotational framework

2012/05/08 by Daoyuang Fang, Bin Han, Fang, Daoyuang +3
Engineering · Mathematics · #35Q35 #76D03 #76D05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1205.1561

openalex publication_date 2012/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 the Fourier-Besov space FB_p,r^2-3/p(\R³), where p ∈ (1,∞] and r ∈ [1,∞]. In the two-dimensional setting, a unique, global mild solution to this set of equations exists for \em non-small initial data u₀ ∈ L^p_σ(\R²) for p ∈ [2,∞).

Citations

• Regularity and integrability of 3D Euler and Navier–Stokes equations for rotating fluids

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