Differential and Integral Equations

On local $L_p$-$L_q$ well-posedness of incompressible two-phase flows with phase transitions: the case of non equal densities

Senjoi Shimizu and Shintaro Yagi

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Abstract

The basic model for incompressible two-phase flows with phase transitions where the interface is nearly flat in the case of non-equal densities is considered. The local well-posedness of the model in $L_p$-setting was proved in Prüss and Shimizu [14]. In this paper, we prove local well-posedness of the model $L_p$ in time $L_q$ in space settting.

Article information

Source
Differential Integral Equations, Volume 28, Number 1/2 (2015), 29-58.

Dates
First available in Project Euclid: 11 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.die/1418310420

Mathematical Reviews number (MathSciNet)
MR3299116

Zentralblatt MATH identifier
1363.35378

Subjects
Primary: 35R35: Free boundary problems 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76D45: Capillarity (surface tension) [See also 76B45] 76T10: Liquid-gas two-phase flows, bubbly flows

Citation

Shimizu, Senjoi; Yagi, Shintaro. On local $L_p$-$L_q$ well-posedness of incompressible two-phase flows with phase transitions: the case of non equal densities. Differential Integral Equations 28 (2015), no. 1/2, 29--58. https://projecteuclid.org/euclid.die/1418310420


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