arXiv subjects

Yuebo Cao

Publications and source records attributed to Yuebo Cao.

4 recordsLinked to original sources

arXiv2026

Global boundedness and asymptotic behavior of the chemotaxis system for Alopecia Areata with weakly singular sensitivity

This paper considers the homogeneous Neumann initial-boundary value problem for Alopecia Areata chemotaxis model with weakly singular sensitivity. For any appropriately regular initial conditions,it is shown that the problem admits a global boundedness of classical solutions in two spatial dimensions. Moreover, through the explicit construction of Lyapunov functions, we establish that the globally bounded solution converges exponentially to a constant steady state. The paper concludes with numerical experiments that serve to visually illustrate and corroborate some of the theoretically derived findings.

math.AP↗

arXiv2021

Global Classical Solutions to the Compressible Navier-Stokes Equations with Navier-type slip Boundary Condition in 2D Bounded Domains

We study the barotropic compressible Navier-Stokes equations with Navier-type boundary condition in a two-dimensional simply connected bounded domain with $C^{\infty}$ boundary $\partialΩ.$ By some new estimates on the boundary related to the Navier-type slip boundary condition, the classical solution to the initial-boundary-value problem of this system exists globally in time provided the initial energy is suitably small even if the density has large oscillations and contains vacuum states. Futhermore, we also prove that the oscillation of the density will grow unboundedly in the long run with an exponential rate provided vacuum (even a point) appears initially. As we known, this is the first result concerning the global existence of classical solutions to the compressible Navier-Stokes equations with Navier-type slip boundary condition and the density containing vacuum initially for general 2D bounded smooth domains.

math.AP↗

arXiv2021

Global Classical Solutions to the 3D Density-Dependent Viscosity Compressible Navier-Stokes Equations with Navier-Slip Boundary Condition in a Simply Connected Bounded Domain

This paper concerns the global existence for classical solutions problem to the 3D Density-Dependent Viscosity barotropic compressible Navier-Stokes in $Ω$ with slip boundary condition, where $Ω$ is a simply connected bounded $C^{\infty}$ domain in $\mathbb{R}^3$ and its boundary only has a finite number of 2-dimensional connected components. By a series of a priori estimates, we show that the classical solution to the system exists globally in time under the assumption that the initial energy is suitably small. The initial density of such a classical solution is allowed to have large oscillations and contain vacuum states. We also adopt some new techniques and methods to obtain necessary a priori estimates, especially the boundary integral terms estimates. This is the first result concerning the global existence of classical solutions to the compressible Navier-Stokes equations with density containing vacuum initially and viscosity coefficients depending on density for general 3D bounded smooth domains.

math.AP↗

arXiv2019

On the Global Strong Solutions to Magnetohydrodynamics with Density-Dependent Viscosity and Degenerate Heat-Conductivity in Unbounded Domains

For the equations of a planar magnetohydrodynamic (MHD) compressible flow with the viscosity depending on the specific volume of the gas and the heat conductivity being proportional to a positive power of the temperature, we obtain global existence of the unique strong solutions to the Cauchy problem or the initial-boundary-value one under natural conditions on the initial data in one-dimensional unbounded domains. Our result generalizes the classical one of the compressible Navier-Stokes system with constant viscosity and heat conductivity ([Kazhikhov. Siberian Math. J. (1982)]) to the planar MHD compressible flow with nonlinear viscosity and degenerate heat-conductivity, which means no shock wave, vacuum, or mass or heat concentration will be developed in finite time, although the interaction between the magnetodynamic effects and hydrodynamic is complex and the motion of the flow has large oscillations.

math.AP↗