4 citations · 16 across the 42 of their papers we have counts for
43 papers
-Unconditional well-posedness for low dispersion fractional KdV equations
Luc Molinet, Weipeng Zhu
We show that the -unconditional well-posedness, that is well-known for the KdV equation, is shared by KdV type equations with weaker dispersion. This is despite…
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…
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…
Non-uniform convergence of solution for the Camassa-Holm equation in the zero-filter limit
Jinlu Li, Yanghai Yu, Weipeng Zhu
In the short note, we prove that given initial data with and for some , the solution of the Camassa-Holm equation does no…
Anomalous Dissipation for the d-dimensional Navier-Stokes Equations
Jinlu Li, Yanghai Yu, Weipeng Zhu
The purpose of this paper is to study the vanishing viscosity limit for the d-dimensional Navier--Stokes equations in the whole space: \begin{equation*} \begin{cases} \partial_tu^\…
Loss of Uniform Convergence for Solutions of the Navier--Stokes Equations in the Inviscid Limit
Jinlu Li, Yanghai Yu, Weipeng Zhu
In this paper, we consider the inviscid limit problem to the higher dimensional incompressible Navier--Stokes equations in the whole space. It is shown in [Guo, Li, Yin: J. Funct.…
On the well-posedness and non-uniform continuous dependence for the Novikov equation in the Triebel-Lizorkin spaces
Jinlu Li, Yanghai Yu, Weipeng Zhu
In this paper we study the Cauchy problem of the Novikov equation in for initial data belonging to the Triebel-Lizorkin spaces, i.e, with $1< p, r…
Ill-posedness for the periodic Camassa--Holm type equations in the end-point critical Besov space
Jinlu Li, Yanghai Yu, Weipeng Zhu
For the real-line case, it is shown that both the Camassa--Holm \cite{Guo} and Novikov equations \cite{Li-arx} are ill-posed in . In this paper, by presenting a n…
Ill-posedness for a generalized Camassa-Holm equation with higher-order nonlinearity in the critical Besov space
Wei Deng, Min Li, Xing Wu +1
In this paper, we prove that the Cauchy problem for a generalized Camassa-Holm equation with higher-order nonlinearity is ill-posed in the critical Besov space …
Zero-filter limit for the Camassa-Holm equation in Sobolev spaces
Jinlu Li, Yanghai Yu, Weipeng Zhu
The aim of this paper is to answer the question left in \cite{GL} (Math. Z. (2015) 281). We prove that the zero-filter limit of the Camassa-Holm equation is the Burgers equation in…
Ill-posedness of the Novikov equation in the critical Besov space
Jinlu Li, Yanghai Yu, Weipeng Zhu
It is shown that both the Camassa-Holm and Novikov equations are ill-posed in with in \cite{Guo2019} and well-pos…
Norm inflation and ill-posedness for the Fornberg-Whitham equation
Jinlu Li, Xing Wu, Yanghai Yu +1
In this paper, we prove that the Cauchy problem for the Fornberg-Whitham equation is not locally well-posed in with $(s,p,r)\in (1,1+\frac1p)\times[2,\infty)\times…
Nowhere-uniform continuity of the solution map of the Camassa-Holm equation in Besov spaces
Jinlu Li, Yanghai Yu, Weipeng Zhu
In the paper, we gave a strengthening of our previous work in [32] (J. Differ. Equ. 269 (2020)) and proved that the data-to-solution map for the Camassa-Holm equation is nowhere un…
Ill-posedness issue on a multidimensional chemotaxis equations in the critical Besov spaces
Jinlu Li, Yanghai Yu, Weipeng Zhu
In this paper, we aim to solving the open question left in [Nie, Yuan: Nonlinear Anal 196 (2020); J. Math. Anal. Appl 505 (2022)) and Xiao, Fei: J. Math. Anal. Appl 514 (2022)]. We…
Ill-posedness for the stationary Navier-Stokes equations in critical Besov spaces
Jinlu Li, Yanghai Yu, Weipeng Zhu
This paper presents some progress toward an open question which proposed by Tsurumi (Arch. Ration. Mech. Anal. 234:2, 2019): whether or not the stationary Navier-Stokes equations i…
Ill-posedness for the two component Degasperis-Procesi equation in critical Besov space
Jinlu Li, Min Li, Weipeng Zhu
In this paper, we study the Cauchy problem for the two component Degasperis-Procesi equation in critical Besov space . By presenting a new construction o…
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…
Non-uniform dependence on initial data for the Camassa--Holm equation in Besov spaces: Revisited
Jinlu Li, Yanghai Yu, Weipeng Zhu
In the paper, we revisit the uniform continuity properties of the data-to-solution map of the Camassa--Holm equation on the real-line case. We show that the data-to-solution map of…
Sharp ill-posedness for the generalized Camassa-Holm equation in Besov spaces
Jinlu Li, Yanghai Yu, Weipeng Zhu
In this paper, we consider the Cauchy problem for the generalized Camassa-Holm equation that includes the Camassa-Holm as well as the Novikov equation on the line. We present a new…
Well-posedness and Continuity Properties of the Degasperis-Procesi equation in critical Besov space
Jinlu Li, Yanghai Yu, Weipeng Zhu
In this paper, we obtain the local-in-time existence and uniqueness of solution to the Degasperis-Procesi equation in . Moreover, we prove that the data-to-solu…
Ill-posedness for the Camassa-Holm and related equations in Besov spaces
Jinlu Li, Yanghai Yu, Weipeng Zhu
In this paper, we give a construction of such that corresponding solution to the Camassa-Holm equation starting from is discontinuous at in th…
Ill-posedness for the Euler equations in Besov spaces
Jinlu Li, Yanghai Yu, Weipeng Zhu
In the paper, we consider the Cauchy problem to the Euler equations in with . We construct an initial data showing that the correspon…
Ill-posedness for the Burgers equation in Sobolev spaces
Jinlu Li, Yanghai Yu, Weipeng Zhu
In this paper, we considered the Cauchy problem for the Burgers equation and proved that the problem is ill-posed in Sobolev spaces with $s\in[1,\fr32)$.