2009/05/30 by Igor A. Tanski, Tanski, Igor A.
Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical functions and polynomials #Nonlinear Waves and Solitons #nlin.CD #nlin.SI
paper · pdf · doi:10.48550/arxiv.0906.0070
18 pages, 3 tables, TeX
arxiv created 2009/05/30 · openalex publication_date 2009/05/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we construct algebraic equation for elements of spectrum of linearized Fokker - Planck differential operator for incompressible fluid. We calculate roots of this equation using simple numeric method. For all these roots real part is positive, that is corresponding solutions are damping. Eigenfunctions of linearized Fokker - Planck differential operator for incompressible fluid are expressed as linear combinations of eigenfunctions of usual Fokker - Planck differential operator. Poisson's equation for pressure is derived from incompressibility condition. It is stated, that the pressure could be totally eliminated from dynamics equations. The Cauchy problem setup and solution method is presented. The role of zero pressure solutions as eigenfunctions for confluent eigenvalues is emphasized.