Abstract
AbstractIn this paper, we are concerned with the free boundary value problem for a model of inviscid liquid‐gas two‐phase flow with radial symmetry. For simplicity, we assume that the gas velocity is always equal to the liquid one and the gas and liquid are both connected continuously to the outer vacuum through the same free boundary. First, we constructed two classes of global analytical solutions by using a self‐similar ansatz. Second, for the general free boundary value problem of this model, we show that the free boundary separating the two‐phase flow from vacuum will spread outward at least linearly in time, provided that the two‐phase fluids motion remains smooth and the initial flow moves outward on average to the vacuum. Third, we present a sufficient condition for the blowup of smooth solutions to the problem.
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Schedule a callMore From: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
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