Well-posedness of a Navier–Stokes–Cahn–Hilliard system for incompressible two-phase flows with surfactant
| Autor: | Andrea Di Primio, Maurizio Grasselli, Hao Wu |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Mathematical Models and Methods in Applied Sciences. 33:755-828 |
| ISSN: | 1793-6314 0218-2025 |
| DOI: | 10.1142/s0218202523500173 |
| Popis: | We investigate a diffuse-interface model that describes the dynamics of viscous incompressible two-phase flows with surfactant. The resulting system of partial differential equations consists of a sixth-order Cahn–Hilliard equation for the difference of local concentrations of the binary fluid mixture coupled with a fourth-order Cahn–Hilliard equation for the local concentration of the surfactant. The former has a smooth potential, while the latter has a singular potential. Both equations are coupled with a Navier–Stokes system for the (volume averaged) fluid velocity. The evolution system is endowed with suitable initial conditions, a no-slip boundary condition for the velocity field and homogeneous Neumann boundary conditions for the phase functions as well as for the chemical potentials. We first prove the existence of a global weak solution, which turns out to be unique in two dimensions. Stronger regularity assumptions on the initial data allow us to prove the existence of a unique global (respectively, local) strong solution in two (respectively, three) dimensions. In the two-dimensional case, we derive a continuous dependence estimate with respect to the norms controlled by the total energy. Moreover, we establish instantaneous regularization properties of global weak solutions for [Formula: see text]. In particular, we show that the surfactant concentration stays uniformly away from the pure states 0 and 1 after some positive time. |
| Databáze: | OpenAIRE |
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