arXiv subjects

Guo Zhenhua

Publications and source records attributed to Guo Zhenhua.

3 recordsLinked to original sources

arXiv2026

Local-in-time existence of strong solutions to a class of compressible Power-Law flows

We consider a model of the compressible non-Newtonian fluids for power-law flow fulfilling a periodic domain in ${\mathbb R}^3,$ in which the extra stress tensor is induced by a potential with $p(t,x)$-structure. The local-in-time existence of strong solution is proved for all $\frac{7}{5} < \inf p(t,x) \leqslant \sup p(t,x) \leqslant 2.$ Further, an improved blow-up criterion for strong solutions is given in terms of the $L^\infty(0,T;L^3(Ω))$-norm of the gradient of the velocity.

math.AP↗

arXiv2025

Well-posedness for a diffuse interface model of non-Newtonian two-phase flows

The evolution of two partially miscible, nonhomogeneous, incompressible viscous fluids of non-Newtonian type, can be governed by the Navier-Stokes-Cahn-Hilliard system. In the present work, we prove the global existence of weak solutions for the case of initial density containing zero and the concentration depending viscosity with free energy potential equal to the Landau potential in a bounded domain of three dimensions. Furthermore, we show that a strong solutions exist locally in time in the case of three dimensions periodic domain ${\mathbb T}^3.$ The proof relies on a suitable semi-Galerkin scheme and the monotonicity method.

math.AP↗

arXiv2024

Global well-posedness of the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system with Landau Potential

A diffuse-interface model that describes the dynamics of nonhomogeneous incompressible two-phase viscous flows is investigated in a bounded smooth domain in ${\mathbb R}^3.$ The dynamics of the state variables is described by the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system. We first give a blow-up criterion of local strong solution to the initial-boundary-value problem for the case of initial density away from zero. After establishing some key a priori with the help of the Landau Potential, we obtain the global existence and decay-in-time of strong solution, provided that the initial date $\|\nabla u_0\|_{L^{2}(Ω)}+\|\nabla μ_0\|_{L^{2}(Ω)}+ρ_0$ is suitably small.

math.AP↗