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math.AP2006★ 217 cited
A new Bernstein's Inequality and the 2D Dissipative Quasi-Geostrophic Equation
Qionglei Chen, Changxing Miao, Zhifei Zhang
We show a new Bernstein's inequality which generalizes the results of Cannone-Planchon, Danchin and Lemarié-Rieusset. As an application of this inequality, we prove the global well…
math.AP2006★ 49 cited
Well-posedness for the viscous shallow water equations in critical spaces
Qionglei Chen, Changxing Miao, Zhifei Zhang
In this paper, we prove the existence and uniqueness of the solutions for the 2D viscous shallow water equations with low regularity assumptions on the initial data as well as the…