arXiv subjects

Shuxing Zhang

Publications and source records attributed to Shuxing Zhang.

3 recordsLinked to original sources

arXiv2026

Global well-posedness and large-time behavior of the compressible Navier-Stokes equations with hyperbolic heat conduction

The classical Fourier's law, which states that the heat flux is proportional to the temperature gradient, induces the paradox of infinite propagation speed for heat conduction. To accurately simulate the real physical process, the hyperbolic model of heat conduction named Cattaneo's law was proposed, which leads to the finite speed of heat propagation. A natural question is that whether the large-time behavior of the heat flux for compressible flow would be different for these two laws. In this paper, we aim to address this question by studying the global well-posedness and optimal time-decay rates of classical solutions to the compressible Navier-Stokes system with Cattaneo's law. By designing a new method, we obtain the optimal time-decay rates for the highest derivatives of the heat flux, which cannot be derived for the system with Fourier's law by Matsumura and Nishida [Proc. Japan Acad. Ser. A Math. Sci., 55(9):337-342, 1979]. In this sense, our results first reveal the essential differences between the two laws.

math.AP↗

arXiv2026

The combined non-equilibrium diffusion and low Mach number limits of the compressible Navier-Stokes-Fourier-P1 approximation radiation model

In this paper, we investigate the combined non-equilibrium diffusion and low Mach number limits of the compressible Navier-Stokes-Fourier-P1 (NSF-P1) model with general initial data, which arises in the radiation hydrodynamics. Compared to the classical compressible Navier-Stokes-Fourier system, the NSF-P1 model has an asymmetric singular structure caused by the radiation field. To handle these singular terms, we introduce an equivalent pressure and an equivalent velocity to balance the order of singularity and establish the uniform estimates of solutions by designating appropriate weighted norms as well as carrying out delicate energy analysis. We conclude that, for partially general initial data and the strong scattering effect, the NSF-P1 model converges to the system of low Mach number heat-conducting viscous flows coupled with a diffusion equation. We also discuss the variations of the limit equations as the scattering intensity changes. Furthermore, when the scattering effect is sufficiently weak, we can obtain the singular limits of the NSF-P1 model with fully general initial data.

math.AP↗

arXiv2025

Well-Posedness and Asymptotic Decay of Solutions to the Three-Dimensional Euler Equations with Damping

The global well-posedness of the multi-dimensional compressible Euler equations with damping remains a longstanding open problem. This problem has been partially resolved in the isentropic regime ({\it i.e.}, the adiabatic exponent $\gamma>1$) for small smooth initial data (see \cite{WY, STW}). In this paper, we establish the global well-posedness and asymptotic decay of smooth solutions of the Cauchy problem of the three-dimensional compressible Euler equations with damping for the isentropic regime $\gamma>1$ and the isothermal regime $\gamma=1$, allowing for partially large initial data. More precisely, the $L^2$-norm of the initial data is allowed to be large, while the third-order Sobolev norm of the initial data is assumed to be small. For the isentropic case, we develop a new analytical framework in which all required {\it a priori} estimates of solution $(\rho,u)$ can be derived under the condition that $\int_0^T \big( \|\nabla\rho\|_{L^\infty} + \|\nabla u\|_{L^\infty} \big) \, \mathrm{d}t$ remains sufficiently small. Moreover, we obtain the optimal algebraic decay rates of global solutions. Furthermore, we study the isothermal limit of solutions of the isentropic regime as $\gamma \to 1$, and establish the global well-posedness and asymptotic decay of solutions to the isothermal Euler equations with damping.

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