不可压缩流体线性化Fokker-Planck方程的解
Solution of linearized Fokker - Planck equation for incompressible fluid
摘要：
本文构造了不可压缩流体线性化Fokker-Planck微分算子谱元的代数方程。我们用简单的数值方法计算了这个方程的根。对于所有这些根，实部都是正的，即相应的解是阻尼的。将不可压流体的线性化Fokker-Planck微分算子的本征函数表示为通常Fokker-Planck微分算子本征函数的线性组合。由不可压缩性条件导出了压力的泊松方程。它指出，压力可以从动力学方程中完全消除。给出了Cauchy问题的建立和求解方法。零压力的解决方案的合流本征值的本征函数的作用被强调。
英文摘要：
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.
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