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math.AP2017
Ill-posedness for the 2D viscous shallow water equations in the critical Besov spaces
Jinlu Li, Pingzhou Hong, Weipeng Zhu
In this paper, we prove that the 2D viscous shallow water equations is ill-posed in the critical Besov spaces $\B^{\frac2p-1}_{p,1}(\R^2)$ with . Our proof mainly depends on t…
math.AP2017
Ill-posedness for the Hamilton-Jacobi equation in Besov spaces
Jinlu Li, Weipeng Zhu, Zhaoyang Yin
In this paper, we study the Cauchy problem for the following Hamilton-Jacobi equation \bbal\bca \pa_tu-\De u=|\na u|^2,\quad t>0, \ x\in \R^d,\\ u(0,x)=u_0, \quad \quad x\in \R^d.…