Abstract
This brief review presents most important results of the authors dealing with mathematical models for the nonstationary two-phase flow of a dusty gas. We do not aim to analyze physical justifications and numerical simulations of dusty gas flows; our attention is focused on the qualitative properties of these models, such as local and global in time well-posedness, uniqueness and asymptotic behavior ofsolutions.
Highlights
Larkin abstract: This brief review presents most important results of the authors dealing with mathematical models for the nonstationary two-phase flow of a dusty gas
We do not aim to analyze physical justifications and numerical simulations of dusty gas flows; our attention is focused on the qualitative properties of these models, such as local and global in time well-posedness, uniqueness and asymptotic behavior of solutions
Distributed between phases according to its volume fraction
Summary
If spherical dust particles of radius r are used in the model, K is given by the Stokes drag formula as 6πμ0r, where μ0 denotes the dynamic viscosity of a clean gas, [16,1] The eigenvalues of this matrix are real: λ1,2 = u ± p , λ3,4 = v, the third component of corresponding eigenvectors is equal to zero; system (2.1)-(2.4) is not hyperbolic. The precise description of behavior of solutions for the opposite situation (eigenvectors do not form a basis) was lacking, probably due to nonlinearity of the equations. This situation can be illustrated by the following simple example. Proof: The proof can be found in [2]
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