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math.AP2022
Ricci Flow method in the existence problem of the K"ahler-Einstein metrics
Liu Chao
This note illustrates the Ricci flow method based on the Cao.H.D's paper[1] and Yau.S.T's paper[4], and tries to explain the method in detail, especially in some calculations. Jian…
math.AP2022★ 1 cited
Blowups for a class of second order nonlinear hyperbolic equations: A reduced model of nonlinear Jeans instability
Chao Liu
Understanding the formation of nonlinear structures in the universe and stellar systems is crucial. The nonlinear Jeans instability plays a key role in these formation processes. I…
math.AP2022★ 4 cited
Rigorous proof of slightly nonlinear Jeans instability in the expanding Newtonian universe
Chao Liu, Yiqing Shi
Due to the nonlinearity of the Euler{Poisson equations, it is possible that the nonlinear Jeans instability may lead to a faster density growing rate than the rate in the standard…