Document Zbl 1395.35162

Well-posedness in critical spaces for a multi-dimensional compressible viscous liquid-gas two-phase flow model. (English) Zbl 1395.35162

Discrete Contin. Dyn. Syst., Ser. B 23, No. 4, 1395-1410 (2018).

Summary: This paper is dedicated to the study of the Cauchy problem for a compressible viscous liquid-gas two-phase flow model in \(\mathbb{R}^N(N\geq2)\). We concentrate on the critical Besov spaces based on the \(L^p\) setting. We improve the range of Lebesgue exponent \(p\), for which the system is locally well-posed, compared to [F. Xu and J. Yuan, Z. Angew. Math. Phys. 66, No. 5, 2395–2417 (2015; Zbl 1327.76154)]. Applying Lagrangian coordinates is the key to our statements, as it enables us to obtain the result by means of Banach fixed point theorem.

Cited in 1 Document

MSC:

35Q35	PDEs in connection with fluid mechanics
76N10	Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics

Keywords:

liquid-gas two-phase flow model; local well-posedness; critical Besov spaces; Lagrangian coordinates

Citations:

Zbl 1327.76154

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References:

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