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Boltzmann equation and hydrodynamics beyond Navier-Stokes.

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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

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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.