Abstract
We make some considerations over the Fokker-Planck equation ɛΔu − div (uX) = 0, associated to a vector field X on the sphere S n , obtaining its steady state in cases non Fokker-Planck integrable, proving also that if X is a polynomial vector field, then the sequences {f i } developing the solution of this equation like \(u_\varepsilon = 1 + \sum\nolimits_{i = 1}^\infty {\frac{{f_i }} {{e^i }}}\) are also polynomials.
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References
J. Guíñez et al., Calculating steady states for a Fokker-Planck equation, Acta Math. Hungar., 91 (2001), 311–323.
A. Rueda, A class of vector fields which are Fokker-Planck integrable, Annales Univ. Sci. Budapest., (1993), 133–137.
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Guíñez, J., Rueda, A.D. Steady states for a Fokker-Planck equation on S n . Acta Math Hung 94, 211–221 (2002). https://doi.org/10.1007/s10474-002-0004-5
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DOI: https://doi.org/10.1007/s10474-002-0004-5