arXiv subjects

Suhua Lai

Publications and source records attributed to Suhua Lai.

2 recordsLinked to original sources

arXiv2024

Stability and Sharp Decay Estimates for 3D MHD Equations with Only Vertical Dissipation Near a Background Magnetic Field

This paper is concerned with the stability and large-time behavior of 3D incompressible MHD equations with only vertical dissipation near a background magnetic field. By making full use of the dissipation generated by the background magnetic field, we first establish the global stability of the solutions in $H^3$-norm. Then, the optimal decay rates of the solutions are obtained, which are consistent with the 2D classical heat equation. Moreover, some enhanced decay rates of $(u_1,b_1)$ are also achieved. In other words, the decay estimates of the second or third component of velocity/magnetic field coincide with those of 2D heat kernel, while the first component behaves like the 3D heat kernel. This is mainly due to the divergence-free condition and the anisotropic structure. The results obtained improve the previous ones due to Lin-Wu-Zhu [24,25].

math.AP↗

arXiv2021

Well-Posedness and Exponential Decay for the Navier-Stokes Equations of Viscous Compressible Heat-Conductive Fluids with Vacuum

This paper is concerned with the Cauchy problem of Navier-Stokes equations for compressible viscous heat-conductive fluids with far-field vacuum at infinity in $\R^3$. For less regular data and weaker compatibility condition than those proposed by Cho-Kim \cite{CK2006}, we first prove the existence of local-in-time solutions belonging to a larger class of functions in which the uniqueness can be shown to hold. The local solution is in fact a classical one away from the initial time, provided the initial density is regular. We also establish the global well-posedness of classical solutions with large oscillations and vacuum in the case when the initial total energy is suitably small. The exponential decay estimates of the global solutions are obtained.

math.AP↗