8 papers
Norm inflation and low-regularity ill-posedness for the rod equation
Jinlu Li, Yanghai Yu
In this paper, we consider the Cauchy problem for the rod equation in the line. By constructing an explicit smooth initial data, we present a new method to prove that this problem…
On the continuous properties for the 3D incompressible rotating Euler equations
Jinlu Li, Yanghai Yu, Neng Zhu
In this paper, we consider the Cauchy problem for the 3D Euler equations with the Coriolis force in the whole space. We first establish the local-in-time existence and uniqueness o…
Nonexistence of Hölder continuous solution for the Camassa-Holm equation in Besov spaces
Yanghai Yu, Jinlu Li, Weipeng Zhu
In the paper, we show that the continuity of the solution can not be improved to the Hölder continuity. Precisely speaking, the solution of the Camassa-Holm equation belongs to $\…
A new proof of unboundedness of Riesz operator in and applications to mild ill-posedness in of the Euler type equations
Jinlu Li, Yanghai Yu
In this paper, we first present a new and simple proof of unboundedness of Riesz operator in and then establish the mild ill-posedness in of 3D rotating E…
Ill-posedness in of the Euler equations: Non-continuous dependence
Jinlu Li, Yanghai Yu
In this paper, we solve an open problem left in the monographs \cite[Bahouri-Chemin-Danchin, (2011)]{BCD}. Precisely speaking, it was obtained in \cite[Theorem 7.1 on pp293, (2011)…
Ill-posedness and inviscid limit of basic equations of fluid dynamics in Besov spaces
Jinlu Li, Xing Wu, Yanghai Yu
In this paper, we consider the Cauchy problem to the basic equations of fluid dynamics on the torus. Firstly, we construct a new initial data and provide a simple proof on the ill-…