TY - JOUR
T1 - A computer-assisted proof for the Kolmogorov flows of incompressible viscous fluid
AU - Watanabe, Yoshitaka
N1 - Funding Information:
We would like to thank the referees for many helpful insights and comments. This work was supported by a Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan (Nos. 18540127, 15204007, 16104001).
PY - 2009/1/15
Y1 - 2009/1/15
N2 - A computer-assisted proof of non-trivial steady-state solutions for the Kolmogorov flows is described. The method is based on the infinite-dimensional fixed-point theorem using Newton-like operator. This paper also proposes a numerical verification algorithm which generates automatically on a computer a set including the exact non-trivial solution with local uniqueness. All discussed numerical results take into account the effects of rounding errors in the floating point computations.
AB - A computer-assisted proof of non-trivial steady-state solutions for the Kolmogorov flows is described. The method is based on the infinite-dimensional fixed-point theorem using Newton-like operator. This paper also proposes a numerical verification algorithm which generates automatically on a computer a set including the exact non-trivial solution with local uniqueness. All discussed numerical results take into account the effects of rounding errors in the floating point computations.
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U2 - 10.1016/j.cam.2008.03.034
DO - 10.1016/j.cam.2008.03.034
M3 - Article
AN - SCOPUS:56949087917
VL - 223
SP - 953
EP - 966
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
IS - 2
ER -