Resonance for the isothermal system of isentropic gas dynamics

Lu, Yufeng

doi:10.1090/s0002-9939-2011-10733-0

Cited by 3 publications

(1 citation statement)

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“…For the case of nozzle flow without the friction, namely b(x, t) = 0 and α(x, t) = 0, the global solution of the Cauchy problem was well studied (cf. [1,2,7,9] and the references cited therein); When a(x) = 0 and α(x, t) = 0, the source term b(x, t) in System ( 1) is corresponding to an outer force [3,8], and when b(x, t) = 0, a(x) = 0, α(x, t)u|u| in (1) corresponds physically to a friction term [5].…”

Section: Introductionmentioning

confidence: 99%

Soluciones globales para sistema isotérmico con fuente

Wang¹

2021

Rev Integr temas mat

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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+(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. Let-ters, 95(2019), 35-40) and “Existence of Global Solutions for Isentropic GasFlow with Friction” (Nonlinearity, 33(2020), 3940-3969), where the global solution was obtained for the source f(x,t,ρ,u)=(a′(x)/a(x))*ρu^2, f(x,t,ρ,u)=b(x,t)ρ, f(x,t,ρ,u)=α(x,t)ρu|u| respectively.

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