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Abstract
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In this talk I will present some recent results on global regularity problems to some Navier-Stokes type models. In the first part, we show the global-in-time existence of regular solution to some Navier-Stokes equations with mass diffusion in the two dimensional case. In the second part we will discuss some regularity criterion to the compressible Navier-Stokes-Fourier system. These works are joint collaborated with X. Cai, E. Feireisl, A. Novotny, C. Wang and Z. Zhang.
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