arXiv subjects

Yanfang Peng

Publications and source records attributed to Yanfang Peng.

6 recordsLinked to original sources

arXiv2025

Nonlinearly Exponential Stability for Lions-Feireisl's Weak Solutions to the Barotropic Compressible Navier-Stokes Equations with Large Potential External Forces

The large time behavior for Lions-Feireisl's finite energy weak solutions to the barotropic compressible Navier-Stokes equations with large potential external forces in three-dimensional (3D) bounded domains is considered. Although the equilibrium state of density is not a constant anymore due to the non-constant external forces, by constructing a suitable Lyapunov functional and using the extra integrability of the density, after expanding the difference of the density and its steady state in a Taylor series with respect to the difference of some power function of density and that of the steady density, it is proved that any Lions-Feireisl's finite energy weak solution would decay exponentially to the equilibrium state as time tends to infinity.

math.AP↗

arXiv2025

On Outer Pressure Problem of Compressible Navier-Stokes System with Degenerate Heat-Conductivity in Unbounded Domains

The compressible Navier-Stokes system with the constant viscosity and the nonlinear heat conductivity which is proportional to a positive power of the temperature and may be degenerate is considered. Under the outer pressure boundary conditions in one-dimensional unbounded spatial domains, the global existence of the strong solutions is obtained after proving that both the specific volume and temperature are bounded from below and above independently of time and space. Moreover, the asymptotically stability of global solutions is established as time tends to infinity.

math.AP↗

arXiv2023

Ground state solutions to a coupled nonlinear logarithmic Hartree system

In this paper, we study the following coupled nonlinear logarithmic Hartree system \begin{align*} \left\{ \displaystyle \begin{array}{ll} \displaystyle -\Delta u+ \lambda_1 u =\mu_1\left( -\frac{1}{2\pi}\ln(|x|) \ast u^2 \right)u+\beta \left( -\frac{1}{2\pi}\ln(|x|) \ast v^2 \right)u, & x \in ~ \mathbb R^2, \vspace{.4cm}\\ -\Delta v+ \lambda_2 v =\mu_2\left( -\frac{1}{2\pi}\ln(|x|) \ast v^2 \right)v +\beta\left( -\frac{1}{2\pi}\ln(|x|) \ast u^2 \right)v, & x \in ~ \mathbb R^2, \end{array} \right.\hspace{1cm} \end{align*} where $\beta, \mu_i, \lambda_i \ (i=1,2)$ are positive constants, $\ast$ denotes the convolution in $\mathbb R^2$. By considering the constraint minimum problem on the Nehari manifold, we prove the existence of ground state solutions for $\beta>0$ large enough. Moreover, we also show that every positive solution is radially symmetric and decays exponentially.

math.AP↗

arXiv2021

Nonlinearly stability of solutions on the outer Pressure Problem of Compressible Navier-Stokes System with Temperature-Dependent Heat Conductivity

In this paper, the one-dimensional compressible Navier-Stokes system with outer pressure boundary conditions is investigated. Under some suitable assumptions, we prove that the specific volume and the temperature are bounded from below and above independently of time, and then give the local and global existence of strong solutions. Furthermore, we also obtain the convergence of the global strong solution to a stationary state and the nonlinearly stability of its convergence. It is worth noticing that all the assumptions imposed on the initial data are the same as Takeyuki Nagasawa [Japan.J.Appl.Math.(1988)]. Therefore, our work can be regarded as an improvement of the results of Takeyuki.

math.AP↗

arXiv2021

On the asymptotic behavior of the one-dimensional motion of the polytropic ideal gas with degenerate heat conductivity

We consider the one-dimensional compressible Navier-Stokes system with constant viscosity and the nonlinear heat conductivity being proportional to a positive power of the temperature which may be degenerate. This problem is imposed on the stress-free boundary condition, which reveals the motion of a viscous heat-conducting perfect polytropic gas with adiabatic ends putting into a vacuum. We prove that the solution of one dimensional compressible Navier-Stokes system with the stress-free boundary condition shares the same large-time behavior as the case of constant heat conductivity.

math.AP↗

arXiv2021

Semi-classical analysis for Fractional Schrödinger Equations with fast decaying potenials

We study the following fractional Schrödinger equation \begin{equation*}\label{eq0.1} ε^{2s}(-Δ)^s u + V(x)u = |u|^{p - 2}u, \,\,x\in\,\,\mathbb{R}^N, \end{equation*} where $s\in (0,\,1)$, $N>2s$, $p>1$ is subcritical and $V(x)$ is a nonnegative continuous potential. We use penalized technique to show that the problem has a family of solutions concentrating at a positive local minimum of $V(x)$ provided that $\frac{2s}{N-2s}+2<p<\frac{2N}{N-2s}$. The novelty is that $V$ can decay arbitrarily or even be compactly supported.

math.AP↗