Abstract

WANG, Xian-Ting. Global Solutions to Isothermal System with Source. Integración - UIS [online]. 2021, vol.39, n.1, pp.51-55.  Epub Feb 28, 2021. ISSN 0120-419X.  https://doi.org/10.18273/revint.v39n1-2021004.

In this short note, we are concerned with the global existence of solutions to the isothermal system with source, where the inhomogeneous terms f(x, t, ρ, u) = b(x, t)ρ + ρu2 + α(x, t)ρu|u| are appeared in the momentum equation. Our work extended the results in the previous papers “Resonance for the Isothermal System of Isentropic Gas Dynamics” (Proc. A.M.S.139(2011),2821-2826), “Global Existence and Stability to the Polytropic Gas Dynamics with an Outer Force” (Appl. Math. Letters, 95(2019), 35-40) and “Existence of Global Solutions for Isentropic Gas Flow with Friction” (Nonlinearity, 33(2020), 3940-3969), where the global solution was obtained for the source f(x, t, ρ, u) = ρu2 , f(x, t, ρ, u) = b(x, t)ρ, f(x, t, ρ, u) = α(x, t)ρu|u| respectively.

Keywords : Global L^∞ solution; isothermal system; source terms; compensated compactness; MSC2010: 35L45; 35L60; 46T99.

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