A note on the regularity of weak solutions to the coupled 2D Allen–Cahn–Navier–Stokes system
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T. Tachim Medjo
Abstract
In this article, we study a coupled Allen–Cahn–Navier–Stokes model in a two-dimensional domain. The model consists of the Navier–Stokes equations for the velocity, coupled with an Allen–Cahn model for the order (phase) parameter. We present an equivalent weak formulation for the model, and we prove a new regularity result for the weak solutions.
Acknowledgements
The author would like to thank the anonymous referees whose comments helped to greatly improve the content of this note.
References
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Articles in the same Issue
- Frontmatter
- Two-step collocation methods for two-dimensional Volterra integral equations of the second kind
- Riesz basis of exponential family for a hyperbolic system
- 𝜎-ideals and outer measures on the real line
- Some fractional differential equations involving generalized hypergeometric functions
- Global existence of solutions to nonlinear Volterra integral equations
- Second-order characterization of convex functions and its applications
- On some k-fractional integral inequalities of~Hermite--Hadamard type for twice differentiable generalized beta (r, g)-preinvex functions
- Refinements of the Hermite–Hadamard inequality for co-ordinated convex mappings
- Fractional Ostrowski type inequalities for functions whose certain power of modulus of the first derivatives are pre-quasi-invex via power mean inequality
- Some families of sublinear correspondences
- Decay rates for a coupled quasilinear system of nonlinear viscoelastic equations
- A note on the regularity of weak solutions to the coupled 2D Allen–Cahn–Navier–Stokes system
