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- W2022280001 abstract "In this paper, we study the global existence of weak solutions for the Cauchy problem of nonhomogeneous system of isentropic gas dynamics (1.1) with bounded initial data (1.2). First, we use the maximum principle to obtain the uniformly bounded L∞ estimate z(ρδ,ε,uδ,ε)≤(B(x),wρδ,ε,uδ,ε)≤M(t) for the ε-viscosity and δ-flux-approximation solutions of (1.1) without the restriction z0(x)≥0 or w0(x)≤0 as given in the paper Klingenberg and Lu (1997) [8], where w,z are Riemann invariants of (1.1) and B(x)>0 is a bounded function of x depending on the function a(x) given in (1.1), but independent of δ,ε. Second, we use the compensated compactness theory and the compact frameworks given in Chen and LeFloch (2003) [18], Ding et al. (1989) [19], DiPerna (1983) [15], Lions et al. (1996) [16], Lions et al. (1994) [17] to prove the global existence of weak solutions for the Cauchy problem (1.1)–(1.2). Third, we extend the existence results of weak solutions for a polytropic gas with γ∈(1,53] in Tsuge (2006) [10] to the general pressure function P(ρ)." @default.
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- W2022280001 date "2011-10-01" @default.
- W2022280001 modified "2023-09-30" @default.
- W2022280001 title "Global existence of solutions to resonant system of isentropic gas dynamics" @default.
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- W2022280001 doi "https://doi.org/10.1016/j.nonrwa.2011.04.005" @default.
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