On an auto-controlled global existence scheme of the incompressible\n Navier Stokes equation

2013/09/18 by Joerg Kampen, Kampen, Joerg
Engineering · Mathematics · #35Q30 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1309.4824

openalex publication_date 2013/09/18 · openalex created_date 2022/09/05 · openalex updated_date 2026/07/28

Abstract

We propose a global scheme for the incompressible Navier Stokes equation,\nwhere at each time step a damping potential term is introduced via a time\ndilation transformation of the equation itself. This leads a global upper\nbounds of the value function and its spatial derivatives. The regularity is\nlimited only by the regularity of the viscosity coefficient function and by the\nregularity and polynomial decay of the data. On an analytical level the scheme\nproposed is an alternative to schemes with external control functions.\n

Citations

• Some infinite matrix analysis, a Trotter product formula for dissipative\n operators, and an algorithm for the incompressible Navier-Stokes equation
• Singular vorticity solutions of the incompressible Euler equation via inviscid limits
• Sur le mouvement d'un liquide visqueux emplissant l'espace

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