Changxing Miao

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In the paper, the large time behavior of solutions of the Cauchy problem for the one dimensional fractal Burgers equation u t + (−∂ 2 x) α/2 u + uu x = 0 with α ∈ (1, 2) is studied. It is shown that if the nondecreasing initial datum approaches the constant states u ± (u − < u +) as x → ±∞, respectively, then the corresponding solution converges toward the(More)
The two-dimensional incompressible Boussinesq equations with partial or fractional dissipation have recently attracted considerable attention and the global regularity issue has been extensively investigated. This paper aims at the global regularity in the case when the dissipation is critical. The critical dissipation refers to α + β = 1 when Λ α ≡ (−Δ) α(More)
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