2009/09/09 by Andrei D. Polyanin, Polyanin, A. D., S. N. Aristov +1
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Computational Fluid Dynamics and Aerodynamics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.0909.1844
openalex publication_date 2009/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Systems of hydrodynamic type equations derived from the Navier-Stokes equations and the boundary layer equations are considered. A transformation of the Crocco type reducing the equation order for the longitudinal velocity component is described. The issues of nonlinear stability of the obtained solutions are studied. It is found that a specific feature of many solutions of the Navier-Stokes equations is instability. The nonlinear instability of solutions is proved by a new exact method, which may be useful for the analysis of other nonlinear physical models and phenomena.