An efficient numerical verification method for the Kolmogorov problem of incompressible viscous fluid

Some computer-assisted proofs of nontrivial steady-state solutions for the Kolmogorov flows are presented. The method is based on the infinite-dimensional fixed-point theorem using a Newton-like operator with a numerical verification algorithm that automatically generates a set that includes the exact nontrivial solution. When discussing the numerical results, we consider the effects of rounding errors in the floating point computations. This is a continuation of our study that was presented in Watanabe (2009).