1970/12/01 by Gerald Rosen · 20 citations
Engineering · Mathematics · #Applied mathematics #Boundary value problem #Classical mechanics #Compressibility #Computational Fluid Dynamics and Aerodynamics #Convergence (economics) #Field (mathematics) #Flow (mathematics) #Fluid Dynamics and Turbulent Flows #Geometry #Incompressible flow #Initial value problem #Mathematical analysis #Mathematical proof #Mathematics #Mechanics #Navier-Stokes equation solutions #Navier–Stokes equations #Physics #Quantum mechanics #Value (mathematics) #Vector field #Weak solution
paper · doi:10.1063/1.1692879
published in The Physics of Fluids 13(12), 2891-2903 (AIP Publishing)
openalex publication_date 1970/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21
Convergence proofs are reported for a general local iteration solution to the Navier-Stokes initial value problem and estimates of the accuracy of the nth iterative approximation are derived. Without appeal to methods of functional analysis, it is shown that a Kiselev-Ladyzhenskaya weak solution is, in fact, a classical solution. Any one of three alternative conditions on the initial velocity field is found to be sufficient to guarantee the existence of a global solution. Breakdown phenomenon which may prevent a local solution from being continued for all t ≥ 0 to a global solution is analyzed. The mathematical theory suggests that breakdown is precluded for a suitably smooth initial velocity field, irrespective of the over-all initial velocity field magnitude.