Resumen de Soluciones globales para sistema isotérmico con fuente.
Xian Ting Wang
- español
En esta nota estamos interesados en la existencia global de soluciones para el sistema isot\'ermico con fuente, donde los términos no homog\'eneos f(x, t, ρ, u) = b(x, t)ρ +\dfrac{a'(x)}{a(x)}+ρu2 + α(x, t)ρu|u| aparecen en la ecuación de momento. Nuestros resultados extienden los presentados en ``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) y ``Existence of Global Solutions for Isentropic Gas Flow with Friction'' (Nonlinearity, 33(2020), 3940-3969), en los cuales la soluci\'on global se obtuvo, respectivamente, para las fuentes 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|.
- English
In this short note, we are concerned with the global existenceof solutions to the isothermal system with source, where the inhomoge-neous termsf(x,t,ρ,u) =b(x,t)ρ+a′(x)a(x)ρu2+α(x,t)ρu|u|are appearedin the momentum equation. Our work extended the results in the previ-ous papers “Resonance for the Isothermal System of Isentropic Gas Dynam-ics” (Proc. A.M.S.139(2011),2821-2826), “Global Existence and Stability tothe Polytropic Gas Dynamics with an Outer Force” (Appl. Math. Let-ters, 95(2019), 35-40) and “Existence of Global Solutions for Isentropic GasFlow with Friction” (Nonlinearity, 33(2020), 3940-3969), where the globalsolution was obtained for the sourcef(x,t,ρ,u) =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.
