Huicheng Yin

activity

20142026

most citedThe shock formation and optimal regularities of the resulting shock curves for 1-D scalar conservation laws

8 citations · 19 across the 20 of their papers we have counts for

collaborators

21 papers

math.AP2026

Global small data radial symmetric solutions of 3D semilinear Euler-Poisson-Darboux equations

Qianqian Li, Qiao Xin, Huicheng Yin

For the 3D semilinear Euler-Poisson-Darboux equation $□ u + \frac{μ}{t} \partial_{t} u = ∣ u ∣^{p}$ , where $t \geq 1$ , $μ > 0$ and $p > 1$ , it is conjectured that there is a critical exponent $p…

math.AP2026

Global classical solutions to 3D irrotational compressible Euler equations of Chaplygin gases with weakly decaying initial data

Mu Gao, Huicheng Yin

We are concerned with the global classical solution problem of 3D compressible isentropic Euler equations of Chaplygin gases \[ \begin{cases} \partial_tρ+ \mathrm{div}(ρv) = 0,\\ \…

math.AP2026

Global existence of small data solutions to 3-D semilinear Euler-Poisson-Darboux equations

Qianqian Li, Huicheng Yin

There is an interesting open question: for $n$ -D ( $n \geq 1$ ) semilinear Euler-Poisson-Darboux equation $\partial_{t}^{2} u - Δ u + \frac{μ}{t} \partial_{t} u = ∣ u ∣^{p}$ , where $t \geq 1$ , $p > 1$ and $μ > 0$ …

math.AP2026

Long time smooth solutions of 3D cubic quasilinear wave systems with small weakly decaying initial data

Mu Gao, Jun Li, Huicheng Yin

For the 3D cubic quasilinear wave system $\square_{c_i} u^i=G^i(u,\partial u,\partial^2u)=\displaystyle\sum_{\substack{0\le|α|,|β|,|γ|\le1 \\ 1\le j,k,l \le m}}g_{αβγ}^{ijkl}\parti…

math.AP2026

Long time smooth solutions of 2-D quadratic quasilinear wave equations in exterior domains with Neumann boundary conditions

Fei Hou, Huicheng Yin, Meng Yuan

For the 3-D quadratic quasilinear wave equations in exterior domains with Dirichlet or Neumann boundary conditions, the global existence or the maximal existence time of small data…

math.AP2025

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III

Qianqian Li, Huicheng Yin

For the $2$ -D semilinear wave equation with scale-invariant damping $□ u + \frac{μ}{t} \partial_{t} u = ∣ u ∣^{p}$ , where $t \geq 1$ , $μ > 0$ and $p > 1$ , it is conjectured that the global smal…

math.AP2025

Formation and construction of large variational shock waves for 1-D $n \times n$ quasilinear hyperbolic conservation systems

Huicheng Yin, Wanqing Zhu

In the paper [Li Jun, Xu Gang, Yin Huicheng, On the blowup mechanism of smooth solutions to 1D quasilinear strictly hyperbolic systems with large variational initial data, Nonlinea…

math.CA2025

Properties and applications of partial multiple weights for fractional integrals

Wang Dinghuai, Yin Huicheng

In this paper, through the introduction of partial multiple weights, we firstly study the related Rubio de Francia extrapolation theorem within the framework of partial Muckenhoupt…

math.AP2025

The critical power of short pulse initial data on the global existence or blowup of smooth solutions to 3-D semilinear Klein-Gordon equations

Jindou Shen, Huicheng Yin

It is well-known that there are global small data smooth solutions for the 3-D semilinear Klein-Gordon equations $□ u + u = F (u, \partial u)$ with cubic nonlinearities. Howe…

math.AP2025

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, II

Daoyin He, Qianqian Li, Huicheng Yin

For the $2$ -D semilinear wave equation with scale-invariant damping $\partial_{t}^{2} u - Δ u + \frac{μ}{t} \partial_{t} u = ∣ u ∣^{p}$ , where $t \geq 1$ and $p > 1$ , in the paper [T. Imai, M. Kato, H. Taka…

math.AP2025

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, I

Li Qianqian, Wang Dinghuai, Yin Huicheng

There is an interesting open question: for the $n$ -D ( $n \geq 1$ ) semilinear wave equation with scale-invariant damping $\partial_{t}^{2} u - Δ u + \frac{μ}{t} \partial_{t} u = ∣ u ∣^{p}$ , where $t \geq 1$ ,…

math.AP2025

Global existence for 2-D wave maps equation in exterior domains

Fei Hou, Huicheng Yin, Meng Yuan

In the paper [H. Kubo, Global existence for exterior problems of semilinear wave equations with the null condition in 2D, Evol. Equ. Control Theory 2 (2013), no. 2, 319-335], for t…

math.AP2024

Global existence and scattering of small data smooth solutions to quasilinear wave systems on $R^{2} \times T$ , II

Fei Hou, Fei Tao, Huicheng Yin

In our previous paper [Fei Hou, Fei Tao, Huicheng Yin, Global existence and scattering of small data smooth solutions to a class of quasilinear wave systems on $\mathbb{R}^2\times\…

math.AP2024

Global existence and scattering of small data smooth solutions to a class of quasilinear wave systems on $R^{2} \times T$

Fei Hou, Fei Tao, Huicheng Yin

In this paper, we are concerned with the global existence and scattering of small data smooth solutions to a class of quasilinear wave systems on the product space $\mathbb{R}^2\ti…

math.AP2024

Global existence of small data weak solutions to the semilinear wave equations with time-dependent scale-invariant damping

Daoyin He, Qianqian Li, Huicheng Yin

In this paper, we are concerned with the global existence of small data weak solutions to the $n -$ dimensional semilinear wave equation $\partial_{t}^{2} u - Δ u + \frac{μ}{t} \partial_{t} u = ∣ u ∣^{p}$ …

math.AP2023★ 1 cited

Almost global solutions of 1D nonlinear Klein-Gordon equations with small weakly decaying initial data

Fei Hou, Fei Tao, Huicheng Yin

It has been known that if the initial data decay sufficiently fast at space infinity, then 1D Klein-Gordon equations with quadratic nonlinearity admit classical solutions up to tim…

math.AP2022★ 5 cited

On the critical exponent $p_{c}$ of the 3D quasilinear wave equation $- (1 + (\partial_{t} ϕ)^{p}) \partial_{t}^{2} ϕ + Δ ϕ = 0$ with short pulse initial data. II, shock formation

Yu Lu, Huicheng Yin

In the previous paper [Ding Bingbing, Lu Yu, Yin Huicheng, On the critical exponent $p_{c}$ of the 3D quasilinear wave equation $- (1 + (\partial_{t} ϕ)^{p}) \partial_{t}^{2} ϕ + Δ ϕ = 0$ with…

math.AP2022★ 5 cited

On the critical exponent $p_{c}$ of the 3D quasilinear wave equation $- (1 + (\partial_{t} ϕ)^{p}) \partial_{t}^{2} ϕ + Δ ϕ = 0$ with short pulse initial data. I, global existence

Bingbing Ding, Yu Lu, Huicheng Yin

For the 3D quasilinear wave equation $- (1 + (\partial_{t} ϕ)^{p}) \partial_{t}^{2} ϕ + Δ ϕ = 0$ with the short pulse initial data $(ϕ,\partial_tϕ)(1,x)=\big(δ^{2-\varepsilon_0}ϕ_0(\frac{r-1}…

math.AP2022

Almost global smooth solutions of the 3D quasilinear Klein-Gordon equations on the product space $R^{2} \times T$

Jun Li, Fei Tao, Huicheng Yin

In the paper, for the 3D quasilinear Klein-Gordon equation with the small initial data posed on the product space $R^{2} \times T$ , we focus on the lower bound of…

math.AP2021★ 8 cited

The shock formation and optimal regularities of the resulting shock curves for 1-D scalar conservation laws

Yin Huicheng, Zhu Lu

The study on the shock formation and the regularities of the resulting shock surfaces for hyperbolic conservation laws is a basic problem in the nonlinear partial differential equa…

math.AP2014

The global smooth symmetric solution to 2-D full compressible Euler system of Chaplygin gases

Ding Bingbing, Witt Ingo, Yin Huicheng

For one dimensional or multidimensional compressible Euler system of polytropic gases, it is well known that the smooth solution will generally develop singularities in finite time…

Global small data radial symmetric solutions of 3D semilinear Euler-Poisson-Darboux equations

Global classical solutions to 3D irrotational compressible Euler equations of Chaplygin gases with weakly decaying initial data

Global existence of small data solutions to 3-D semilinear Euler-Poisson-Darboux equations

Long time smooth solutions of 3D cubic quasilinear wave systems with small weakly decaying initial data

Long time smooth solutions of 2-D quadratic quasilinear wave equations in exterior domains with Neumann boundary conditions

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III

Formation and construction of large variational shock waves for 1-D n×n quasilinear hyperbolic conservation systems

Properties and applications of partial multiple weights for fractional integrals

The critical power of short pulse initial data on the global existence or blowup of smooth solutions to 3-D semilinear Klein-Gordon equations

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, II

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, I

Global existence for 2-D wave maps equation in exterior domains

Global existence and scattering of small data smooth solutions to quasilinear wave systems on R2×T, II

Global existence and scattering of small data smooth solutions to a class of quasilinear wave systems on R2×T

Global existence of small data weak solutions to the semilinear wave equations with time-dependent scale-invariant damping

Almost global solutions of 1D nonlinear Klein-Gordon equations with small weakly decaying initial data

On the critical exponent pc​ of the 3D quasilinear wave equation −(1+(∂t​ϕ)p)∂t2​ϕ+Δϕ=0 with short pulse initial data. II, shock formation

On the critical exponent pc​ of the 3D quasilinear wave equation −(1+(∂t​ϕ)p)∂t2​ϕ+Δϕ=0 with short pulse initial data. I, global existence

Almost global smooth solutions of the 3D quasilinear Klein-Gordon equations on the product space R2×T

The shock formation and optimal regularities of the resulting shock curves for 1-D scalar conservation laws

The global smooth symmetric solution to 2-D full compressible Euler system of Chaplygin gases

Formation and construction of large variational shock waves for 1-D $n \times n$ quasilinear hyperbolic conservation systems

Global existence and scattering of small data smooth solutions to quasilinear wave systems on $R^{2} \times T$ , II

Global existence and scattering of small data smooth solutions to a class of quasilinear wave systems on $R^{2} \times T$

On the critical exponent $p_{c}$ of the 3D quasilinear wave equation $- (1 + (\partial_{t} ϕ)^{p}) \partial_{t}^{2} ϕ + Δ ϕ = 0$ with short pulse initial data. II, shock formation

On the critical exponent $p_{c}$ of the 3D quasilinear wave equation $- (1 + (\partial_{t} ϕ)^{p}) \partial_{t}^{2} ϕ + Δ ϕ = 0$ with short pulse initial data. I, global existence

Almost global smooth solutions of the 3D quasilinear Klein-Gordon equations on the product space $R^{2} \times T$