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Incompressible Navier-Stokes-Fourier Limit from The Boltzmann Equation: Classical Solutions
The global classical solution to the incompressible Navier-Stokes-Fourier equation with small initial data in the whole space is constructed through a zero Knudsen number limit from the solutions to the Boltzmann equation with general collision kernels.The key point is the uniform estimate of the Sobolev norm on the global solutions …