11 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…
The Coriolis effect-induced and ill-posedness in the 3D rotating Euler equations
Jinlu Li, Yanghai Yu
In this paper, we establish the ill-posedness of the 3D rotating Euler equations in endpoint and -based spaces. More precisely, our aim is two fold: (1) we prove…
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 the 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-…
Non-convergence of the Navier-Stokes equations toward the Euler equations in the endpoint Besov spaces
Yanghai Yu, Jinlu Li
In this paper, we consider the inviscid limit problem to the higher dimensional incompressible Navier-Stokes equations in the whole space. It was proved in \cite[J. Funct. Anal., 2…
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…
Global existence and blow-up for the Euler-Poincaré equations with a class of initial data
Jinlu Li, Yanghai Yu, Weipeng Zhu
In this paper we investigate the Cauchy problem of d-dimensional Euler-Poincaré equations. By choosing a class of new and special initial data, we can transform this d-dimensional…
Ill-posedness issue on the Oldroyd-B model in the critical Besov spaces
Jinlu Li, Yanghai Yu, Weipeng Zhu
It is proved in \cite[J. Funct. Anal., 2020]{AP} that the Cauchy problem for some Oldroyd-B model is well-posed in $\B^{d/p-1}_{p,1}(\R^d) \times \B^{d/p}_{p,1}(\R^d)$ with $1\leq…
On the ill-posedness for the Navier--Stokes equations in the weakest Besov spaces
Yanghai Yu, Jinlu Li
It is proved in \cite{IO21} that the Cauchy problem for the full compressible Navier--Stokes equations of the ideal gas is ill-posed in $\dot{B}_{p, q}^{2 / p}(\mathbb{R}^2) \times…
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 $\m…
Ill-posedness for the Camassa-Holm equation in
Jinlu Li, Yanghai Yu, Yingying Guo +1
In this paper, we study the Cauchy problem for the Camassa-Holm equation on the real line. By presenting a new construction of initial data, we show that the solution map in the sm…