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

2025/11/24 by Li, Fang, Mengge, Chang, Zhenhua, Guo
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · doi:10.48550/arxiv.2511.18819

openalex publication_date 2025/11/24 · openalex created_date 2025/11/27 · openalex updated_date 2026/07/28

Abstract

We consider a model of the compressible non-Newtonian fluids for power-law flow fulfilling a periodic domain in \mathbb R³, 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 (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^∞(0,T;L³(Ω))-norm of the gradient of the velocity.

Citations

• Well-posedness for a class of compressible non-Newtonian fluids equations
• Local-in-time existence of strong solutions to a class of compressible\n non-Newtonian Navier-Stokes equations
• Generalized solutions to models of compressible viscous fluids
• Existence of weak solutions for non-stationary flows of fluids with shear thinning dependent viscosities under slip boundary conditions in half space

Related

• Local-in-time existence of strong solutions to a class of compressible\n non-Newtonian Navier-Stokes equations
• Blow-up criterion for a three-dimensional compressible non-Newtonian fluid with vacuum
• On the local well-posedness of strong solutions to the unsteady flows of shear-thinning non-Newtonian fluids with a concentration-dependent power-law index
• Weak solutions and weak-strong uniqueness for a compressible power-law-Oldroyd--B fluid model
• Local existence of strong solutions to the k-ε model equations for turbulent flows