Existence of Global Weak Solutions to a Parabolic p-Laplacian Problem with Convective Term
Abstract
Abstract For a given bounded domain $$\Omega \subset \mathbb R^3$$ Ω ⊂ R 3 , with $$C^2$$ C 2 boundary, and a given instant of time $$T>0$$ T > 0 , we prove the existence of a global weak solution on (0, T ), which satisfies a maximum principle, to a parabolic p -Laplacian system with convective term without divergence constraint for any $$p\in (1,2)$$ p ∈ ( 1 , 2 ) and the initial datum in $$L^\infty (\Omega )$$ L ∞ ( Ω ) . Moreover, we study the finite-time extinction property for suitable initial data.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Advanced Mathematical Physics Problems
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- Journal of Mathematical Fluid Mechanics
- Volume
- 28
- Issue
- 3
- Publication date
- 22 July 2026
- Language
- EN