Yanghai Yu

activity

20182026

most citedA class large solution of the 2D MHD equations with velocity and magnetic damping

16 citations · 38 across the 43 of their papers we have counts for

collaborators

44 papers

math.AP2026

Strong ill-posedness of the 2D Boussinesq equations in supercritical Besov spaces

Jinlu Li, Yanghai Yu

In this paper, we prove that the 2D Boussinesq equations are strongly ill-posed in the supercritical Besov spaces $B_{p, q}^{s}$ and Sobolev spaces $W^{s, p}$ with $(p,q)\in(1,\infty)\…

math.AP2026

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…

math.AP2026

The Coriolis effect-induced $B_{\infty, r}^{s}$ and $B_{1, r}^{s}$ 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 $L^{\infty}$ and $L^{1}$ -based spaces. More precisely, our aim is two fold: (1) we prove…

math.AP2025

Ill-posedness in $B_{p, \infty}^{s}$ 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)…

math.AP2025

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-…

math.AP2025

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…

math.AP2025

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…

math.AP2024

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…

math.AP2024

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…

math.AP2024

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…

math.AP2024

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…

math.AP2023

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 $u_{0} \in H^{s} (R)$ with $s > \frac{3}{2}$ and for some $T > 0$ , the solution of the Camassa-Holm equation does no…

math.AP2023

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^\…

math.AP2023

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.…

math.AP2023

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 $R$ for initial data belonging to the Triebel-Lizorkin spaces, i.e, $u_{0} \in F_{p, r}^{s}$ with $1< p, r…

math.AP2023

Ill-posedness for the periodic Camassa--Holm type equations in the end-point critical Besov space $B_{\infty, 1}^{1}$

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 $B_{\infty, 1}^{1}$ . In this paper, by presenting a n…

math.AP2022

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…

math.AP2022

Ill-posedness of the Novikov equation in the critical Besov space $B_{\infty, 1}^{1} (R)$

Jinlu Li, Yanghai Yu, Weipeng Zhu

It is shown that both the Camassa-Holm and Novikov equations are ill-posed in $B_{p, r}^{1 + 1/ p} (R)$ with $(p, r) \in [1, \infty] \times (1, \infty]$ in \cite{Guo2019} and well-pos…

math.AP2022★ 2 cited

Ill-posedness of the hyperbolic Keller-Segel model in Besov spaces

Xiang Fei, Yanghai Yu, Mingwen Fei

In this paper, we give a new construction of $u_{0} \in B_{p, \infty}^{σ}$ such that the corresponding solution to the hyperbolic Keller-Segel model starting from $u_{0}$ is discontinuous…

math.AP2022

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 $B_{p, r}^{s} (R)$ with $(s,p,r)\in (1,1+\frac1p)\times[2,\infty)\times…

math.AP2022

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…

math.AP2022

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…

math.AP2022

Ill-posedness for the Camassa-Holm equation in $B_{p, 1}^{1} \cap C^{0, 1}$

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…

math.AP2021

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…

Strong ill-posedness of the 2D Boussinesq equations in supercritical Besov spaces

Norm inflation and low-regularity ill-posedness for the rod equation

The Coriolis effect-induced B∞,rs​ and B1,rs​ ill-posedness in the 3D rotating Euler equations

Ill-posedness in Bp,∞s​ of the Euler equations: Non-continuous dependence

Ill-posedness and inviscid limit of the basic equations of fluid dynamics in Besov spaces

Non-convergence of the Navier-Stokes equations toward the Euler equations in the endpoint Besov spaces

On the continuous properties for the 3D incompressible rotating Euler equations

Global existence and blow-up for the Euler-Poincaré equations with a class of initial data

Ill-posedness issue on the Oldroyd-B model in the critical Besov spaces

On the ill-posedness for the Navier--Stokes equations in the weakest Besov spaces

Nonexistence of Hölder continuous solution for the Camassa-Holm equation in Besov spaces

Non-uniform convergence of solution for the Camassa-Holm equation in the zero-filter limit

Anomalous Dissipation for the d-dimensional Navier-Stokes Equations

Loss of Uniform Convergence for Solutions of the Navier--Stokes Equations in the Inviscid Limit

On the well-posedness and non-uniform continuous dependence for the Novikov equation in the Triebel-Lizorkin spaces

Ill-posedness for the periodic Camassa--Holm type equations in the end-point critical Besov space B∞,11​

Zero-filter limit for the Camassa-Holm equation in Sobolev spaces

Ill-posedness of the Novikov equation in the critical Besov space B∞,11​(R)

Ill-posedness of the hyperbolic Keller-Segel model in Besov spaces

Norm inflation and ill-posedness for the Fornberg-Whitham equation

Ill-posedness issue on a multidimensional chemotaxis equations in the critical Besov spaces

Ill-posedness for the stationary Navier-Stokes equations in critical Besov spaces

Ill-posedness for the Camassa-Holm equation in Bp,11​∩C0,1

Non-uniform dependence on initial data for the Camassa--Holm equation in Besov spaces: Revisited

The Coriolis effect-induced $B_{\infty, r}^{s}$ and $B_{1, r}^{s}$ ill-posedness in the 3D rotating Euler equations

Ill-posedness in $B_{p, \infty}^{s}$ of the Euler equations: Non-continuous dependence

Ill-posedness for the periodic Camassa--Holm type equations in the end-point critical Besov space $B_{\infty, 1}^{1}$

Ill-posedness of the Novikov equation in the critical Besov space $B_{\infty, 1}^{1} (R)$

Ill-posedness for the Camassa-Holm equation in $B_{p, 1}^{1} \cap C^{0, 1}$