Smooth solutions of the Euler and Navier-Stokes equations from the a posteriori analysis of approximate solutions

2014/05/31 by Carlo Morosi, Livio Pizzocchero · 2 citations
Mathematics · #math.AP #msc:35Q30 #msc:76D03 #msc:76D05

paper · pdf · doi:10.1016/j.na.2014.10.005

published as Nonlinear Analysis 113 (2015), 298-308 · Author's note. Some overlaps with our previous works arXiv:1402.0487, arXiv:1310.5642, arXiv:1304.2972, arXiv:1203.6865, arXiv:1104.3832, arXiv:1009.2051, arXiv:1007.4412, arXiv:0909.3707, arXiv:0709.1670; these overlaps aim to make the paper self-contained and do not involve the main results. Final version to appear in Nonlinear Analysis

arxiv created 2014/10/27 · arxiv updated 2014/11/21

Abstract

The main result of [C. Morosi and L. Pizzocchero, Nonlinear Analysis, 2012] is presented in a variant, based on a Cⁱnfinity formulation of the Cauchy problem; in this approach, the a posteriori analysis of an approximate solution gives a bound on the Sobolev distance of any order between the exact and the approximate solution.

Citations

• A posteriori estimates for Euler and Navier-Stokes equations
• On the Reynolds number expansion for the Navier-Stokes equations
• On power series solutions for the Euler equation, and the Behr-Necas-Wu initial datum
• On approximate solutions of the incompressible Euler and Navier-Stokes equations
• On the constants in a Kato inequality for the Euler and Navier-Stokes equations
• On the constants in a basic inequality for the Euler and Navier-Stokes equations
• An H¹ setting for the Navier-Stokes equations: quantitative estimates
• On approximate solutions of semilinear evolution equations II. Generalizations, and applications to Navier-Stokes equations

Cited by

• On approximate solutions of the equations of incompressible magnetohydrodynamics
• Large order Reynolds expansions for the Navier-Stokes equations
• New results on the constants in some inequalities for the Navier-Stokes quadratic nonlinearity

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