Published 2021-05-19
Keywords
- Global L∞ solution,
- isothermal system,
- source terms,
- compensated compactness
How to Cite
Copyright (c) 2021 Revista Integración, temas de matemáticas
This work is licensed under a Creative Commons Attribution 4.0 International License.
Abstract
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 +\dfrac{a'(x)}{a(x)}+ρu^{2} + 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) = \dfrac{a'(x)}{a(x)}+ρu2, f(x, t, ρ, u) = b(x, t)ρ, f(x, t, ρ, u) = α(x, t)ρu|u| respectively.
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References
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