Advances in Differential Equations

On local $L_p$-$L_q$ well-posedness of incompressible two-phase flows with phase transitions: Non-equal densities with large initial data

Senjo Shimizu and Shintaro Yagi

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Abstract

A 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. Local well-posedness of the model in $L_p$ in a time setting $L_q$ in a space setting was proved in [30] under a smallness assumption for the initial data. In this paper, we remove the smallness assumption for the initial data.

Article information

Source
Adv. Differential Equations Volume 22, Number 9/10 (2017), 737-764.

Dates
First available in Project Euclid: 27 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.ade/1495850458

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, Senjo; Yagi, Shintaro. On local $L_p$-$L_q$ well-posedness of incompressible two-phase flows with phase transitions: Non-equal densities with large initial data. Adv. Differential Equations 22 (2017), no. 9/10, 737--764. https://projecteuclid.org/euclid.ade/1495850458


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