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Updated: Feb 13, 2026
10:13
A Microfluidic-based Hydrodynamic Trap for Single Particles
Published on: January 21, 2011
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Boltzmann equation and hydrodynamics beyond Navier-Stokes
1Keldysh Institute for Applied Mathematics, RAS, Moscow, 125047, Russian Federation alexander.bobylev@kau.se.
Summary
This study details a method for deriving higher-order hydrodynamic equations, focusing on the Burnett level and linearized Boltzmann equation. The research highlights the effectiveness of
Area of Science:
- Fluid dynamics
- Mathematical physics
- Kinetic theory
Background:
- Hydrodynamic equations describe fluid behavior.
- Higher-order equations are needed for non-equilibrium systems.
- Existing methods have limitations in accuracy and derivation.
Purpose of the Study:
- To derive and regularize higher-order hydrodynamic equations.
- To present a detailed approach for the Burnett level.
- To analyze accuracy of Navier-Stokes and Burnett approximations.
Main Methods:
- Successive changes of hydrodynamic variables.
- Analysis of the linearized Boltzmann equation.
- Development of 'diagonal' hydrodynamic equations.
Main Results:
- Detailed derivation for the Burnett level is presented.
- The linearized Boltzmann equation is analyzed.
- 'Diagonal' equations yield optimal results for the linearized Boltzmann equation.
- Rigorous accuracy estimates for Navier-Stokes and Burnett approximations are provided.
Conclusions:
- The proposed method effectively derives and regularizes higher-order hydrodynamic equations.
- The 'diagonal' approach is superior for the linearized Boltzmann equation.
- Accuracy of common approximations is rigorously quantified.
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