ON APPROXIMATE SOLUTIONS OF SEMILINEAR EVOLUTION EQUATIONS II: GENERALIZATIONS, AND APPLICATIONS TO NAVIER–STOKES EQUATIONS

DOI10.1142/S0129055X08003407zbMath1162.35004arXiv0709.1670OpenAlexW3100322931MaRDI QIDQ3534189

Carlo Morosi, Livio Pizzocchero

Publication date: 3 November 2008

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.1670

zbMATH Keywords

Galerkin methodtorusexponential time decay

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Theoretical approximation in context of PDEs (35A35) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

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Cites Work

• Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
• On the constants for multiplication in Sobolev spaces
• Existence and uniqueness for a nonlinear fractional differential equation
• On the Navier-Stokes initial value problem. I
• Power series for solutions of the 3D Navier-Stokes system on \(\mathbb R^3\)
• A posteriori regularity of the three-dimensional Navier–Stokes equations from numerical computations
• ON APPROXIMATE SOLUTIONS OF SEMILINEAR EVOLUTION EQUATIONS
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