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A Class of Analytical Solutions to the Vacuum Free Boundary Problem of a Viscous Two-Phase Model with Spherical Symmetry
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DOI：10.1007/s10773-026-06324-2.png)
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Abstract
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In this paper, we consider the vacuum free boundary problem of a viscous two-phase model with spherical symmetry, which consists of two mass equations and a momentum equation with viscosity coefficients of the form mu(n, rho) = (n + rho)(theta) and lambda(n, rho) = (theta - 1)(n + rho)(theta). We take the pressure function as P(n, rho) = n(alpha) + rho(gamma) (alpha >= 1, gamma > 1), where n and rho are the densities of two phases. We provide a class of global analytical solutions to this problem when alpha = gamma = theta = 2. Moreover, we prove that the free boundary spreads out at least sub-linearly in time with the rate of O((1 + t)(1/3)) and not more than linearly in time for the constructed solutions, by using the averaged quantities method.
Keywords:
Analytical solutions
Free boundary
Two-phase model
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