{'fraction_non_alphanumeric': 0.023255813953488372, 'fraction_numerical': 0.0031007751937984496, 'mean_word_length': 4.926605504587156, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Ansätze of codimension one for the Navier – Stokes field and reduction of the Navier – Stokes equation

Finding exact solutions of the Navier–Stokes equations (NSEs) for an incompressible viscous fluid is an actual problem of mathematical physics and hydrodynamics. There are some ways to solve this problem. One of them is a usage of symmetry analysis [1–8]. In this article we construct a complete set of inequivalent ansatze of codimension one for the Navier–Stokes field. Using them, we reduce the NSEs to systems of partial differential equations in three independent variables and study their symmetry properties. It is known that the NSEs