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Martingale solutions to stochastic nonlocal Cahn–Hilliard–Navier–Stokes systems with singular potentials driven by multiplicative noise of jump type.
- Source :
-
Random Operators & Stochastic Equations . Sep2024, Vol. 32 Issue 3, p267-300. 34p. - Publication Year :
- 2024
-
Abstract
- In the diffuse interface theory, the motion of two incompressible viscous fluids and the evolution of their interface are described by the well-known model H. The model consists of the Navier–Stokes equations, nonlinearly coupled with a convective Cahn–Hilliard type equation. Here we consider a stochastic version of the model driven by a noise of Lévy type, and where the standard Cahn–Hilliard equation is replaced by its nonlocal version with a singular (e.g., logarithmic) potential. The case of smooth potentials with arbitrary polynomial growth has been already analyzed in [G. Deugoué, A. Ndongmo Ngana and T. Tachim Medjo, Martingale solutions to stochastic nonlocal Cahn–Hilliard–Navier–Stokes equations with multiplicative noise of jump type, Phys. D 398 2019, 23–68]. Taking advantage of this previous result, we investigate this more challenging and physically relevant case. Global existence of a martingale solution is proved with no-slip and no-flux boundary conditions in both 2D and 3D bounded domains. In the two-dimensional case, we prove the uniqueness of weak solutions when the viscosity is constant. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09266364
- Volume :
- 32
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Random Operators & Stochastic Equations
- Publication Type :
- Academic Journal
- Accession number :
- 179391000
- Full Text :
- https://doi.org/10.1515/rose-2024-2013