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A kind of electrorheological fluid equations with orientated convection terms is considered. If the diffusion coefficient a(x,t)∈C1(QT‾) $a(x,t)\in C^{1}(\overline{Q_{T}})$ is degenerate on the boundary ∂Ω, not only the uniqueness of weak solution is proved, but also the stability of the solutions can be proved without any boundary condition, provided that there are some restrictions on the diffusion...
We shall apply the phase-field method to investigate the dynamics of sea ice growth. The model consists of two parabolic equations. The existence and uniqueness of weak solutions to an initial-boundary value problem of this model is proved. Then the regularity, large-time behavior of solutions are studied, also the existence of global attractor is proved. The main technique in this article is energy...
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