New results on the constants in some inequalities for the Navier-Stokes quadratic nonlinearity

2015/11/30 by Carlo Morosi, Mario Pernici, Livio Pizzocchero · 1 citation
Mathematics · Physics and Astronomy · #math.AP #math-ph #math.MP #msc:76D05 #msc:26D10 #msc:46E35

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published as Applied Mathematics and Computation 308 (2017), 54-72 (in an abridged version) · Author's note. Some overlaps with our previous works arXiv:1405.3421, 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. In comparison with version v1, only minor typographical changes

arxiv created 2017/03/22 · arxiv updated 2017/04/17

Abstract

We give fully explicit upper and lower bounds for the constants in two known inequalities related to the quadratic nonlinearity of the incompressible (Euler or) Navier-Stokes equations on the torus T^d. These inequalities are "tame" generalizations (in the sense of Nash-Moser) of the ones analyzed in the previous works [Morosi and Pizzocchero: CPAA 2012, Appl.Math.Lett. 2013].

Citations

• Smooth solutions of the Euler and Navier-Stokes equations from the a posteriori analysis of approximate solutions
• Large order Reynolds expansions for the Navier-Stokes equations
• 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
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• 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

Related

• On the constants in a basic inequality for the Euler and Navier-Stokes equations
• On the constants in a Kato inequality for the Euler and Navier-Stokes equations
• An H¹ setting for the Navier-Stokes equations: quantitative estimates
• An inequality for solutions of the Navier-Stokes equations in Rn
• On approximate solutions of the incompressible Euler and Navier-Stokes equations