Derivation of Fluid Equations from Boltzmann's Kinetic Theory
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nsoonhui
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Summary
The article rigorously derives the fundamental PDEs of fluid mechanics, including compressible Euler and incompressible Navier-Stokes-Fourier equations, from hard sphere particle systems undergoing elastic collisions. It resolves Hilbert's sixth problem by deriving fluid equations from Newton's laws through Boltzmann's kinetic theory.
Key quotes
· 2 pulledThis resolves Hilbert's sixth problem, as it pertains to the program of deriving the fluid equations from Newton's laws by way of Boltzmann's kinetic theory.
The proof relies on the derivation of Boltzmann's equation on 2D and 3D tori, which is an extension of our previous work.
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