Global-in-time classical solutions exist for the 1D BNSF system with large initial data where specific volume and temperature start positive and bounded away from zero.
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Global Existence of Classical Solutions to Brenner-Navier-Stokes-Fourier System for Large Data
Global-in-time classical solutions exist for the 1D BNSF system with large initial data where specific volume and temperature start positive and bounded away from zero.