On the existence and uniqueness of solution to problems of fluid dynamics on a sphere

DOI10.1016/j.jmaa.2011.10.045zbMath1233.35169OpenAlexW2088077036MaRDI QIDQ662106

Yuri N. Skiba

Publication date: 11 February 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.10.045

zbMATH Keywords

sphereunique solvabilityincompressible fluid dynamics

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Weak solutions to PDEs (35D30) Viscous vortex flows (76D17) Fractional partial differential equations (35R11) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items

Strong solutions for the stochastic Navier-Stokes equations on the 2D rotating sphere with stable Lévy noise, Asymptotic behavior of solutions to barotropic vorticity equation on a sphere, Qualitative properties of solutions to vorticity equation for a viscous incompressible fluid on a rotating sphere

Cites Work

• On the spectral problem in the linear stability study of flows on a sphere
• On the stability of viscous fluid motions
• The best approximation of the classes of functions \(W_ p^{\alpha}(S^ n)\) by polynomials in spherical harmonics
• Approximation of smooth functions on the sphere \(S^ n \)by the Fourier method
• The boundary value problems of mathematical physics. Transl. from the Russian by Jack Lohwater
• Two-dimensional Navier-Stokes flow with measures as initial vorticity
• The Navier-Stokes equation for an incompressible fluid in \(\mathbb{R}^ 2\) with a measure as the initial vorticity
• Instability of the Rossby-Haurwitz wave in the invariant sets of perturbations.
• Uniqueness for the two-dimensional Navier-Stokes equation with a measure as initial vorticity
• Global solutions of two-dimensional Navier-Stokes and Euler equations
• Remarks on the preceding paper by M. Ben-Artzi ``Global solutions of two- dimensional Navier-Stokes and Euler equations
• Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique
• On the behavior of special classes of ultraspherical expansions. I, II
• Investigation of the method of nets for two-dimensional equations of the Navier-Stokes type with non-negative viscosity. II
• Bernstein's inequality for fractional derivatives of polynomials in spherical harmonics
• Singular Integral Operators and Differential Equations
• Linear instability of ideal flows on a sphere
• On the Bernstein-Nikol'skii and Favard inequalities on compact homogeneous spaces of rank 1
• Classical solutions of the nondivergent barotropic equations on the sphere*
• Rate of Convergence Estimates for Nonselfadjoint Eigenvalue Approximations
• Multipliers for Spherical Harmonic Expansions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item