On dispersive effect of the Coriolis force for the stationary Navier-Stokes equations

DOI10.1016/j.jde.2011.01.003zbMath1211.35218arXiv1007.1181OpenAlexW1999865405MaRDI QIDQ2430942

Tsuyoshi Yoneda, Paweł Konieczny

Publication date: 8 April 2011

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.1181

zbMATH Keywords

Fourier transformCoriolis forceBesov spaceslarge datastationary Navier-Stokes equationsdispersive effect

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)

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Cites Work

• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global well-posedness for the 3D rotating Navier-Stokes equations with highly oscillating initial data
• Long-time solvability of the Navier-Stokes equations in a rotating frame with spatially almost periodic large data
• Kelvin's discovery of Taylor columns
• Uniform local solvability for the Navier-Stokes equations with the Coriolis force
• On time analyticity of the Navier-Stokes equations in a rotating frame with spatially almost periodic data
• Global solvability of the Navier-Stokes equations in spaces based on sum-closed frequency sets
• The Fujita-Kato approach to the Navier-Stokes equations in the rotational framework
• Asymptotic behavior of global solutions to the Navier-Stokes equations in \(\mathbb{R}^3\)
• A generalization of a theorem by Kato on Navier-Stokes equations
• Exterior problem for the stationary Navier-Stokes equations in the Lorentz space
• Smooth or singular solutions to the Navier-Stokes system?
• Well-posedness of the Cauchy problem for the fractional power dissipative equations
• Directional approach to spatial structure of solutions to the Navier–Stokes equations in the plane
• Uniform global solvability of the rotating Navier-Stokes equations for nondecaying initial data
• Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
• Gevrey regularity of solutions to the 3-D Navier-Stokes equations with weighted $l_p$ initial data