A blow-up criterion of strong solution to a 3D viscous liquid-gas two-phase flow model with vacuum

DOI10.1016/j.matpur.2011.09.005zbMath1398.76224OpenAlexW2018698958MaRDI QIDQ764910

Changjiang Zhu, Huanyao Wen, Lei Yao

Publication date: 16 March 2012

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2011.09.005

zbMATH Keywords

Navier-Stokes equationsglobal existencelinearized systemlocal strong solution

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Liquid-gas two-phase flows, bubbly flows (76T10) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10)

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Cites Work

• Unnamed Item
• Unnamed Item
• Existence and uniqueness of global weak solution to a two-phase flow model with vacuum
• A blow-up criterion of strong solutions to the 2D compressible Navier-Stokes equations
• A Beale-Kato-Majda blow-up criterion for the 3-D compressible Navier-Stokes equations
• Blowup criterion for viscous baratropic flows with vacuum states
• A blow-up criterion for a 2D viscous liquid-gas two-phase flow model
• Global existence of weak solutions for a viscous two-phase model
• A blow-up criterion for classical solutions to the compressible Navier-Stokes equations
• Global weak solutions for a viscous liquid-gas model with transition to single-phase gas flow and vacuum
• Global weak solutions for a viscous liquid-gas model with singular pressure law
• Free boundary value problem for a viscous two-phase model with mass-dependent viscosity
• Unique solvability of the initial boundary value problems for compressible viscous fluids.
• Global solutions of the Navier-Stokes equations for multidimensional compressible flow with discontinuous initial data
• On existence of global solutions to the two-dimensional Navier-Stokes equations for a compressible viscous fluid
• Existence and Asymptotic Behavior of Global Weak Solutions to a 2D Viscous Liquid-Gas Two-Phase Flow Model
• Serrin-Type Criterion for the Three-Dimensional Viscous Compressible Flows
• Computational Methods for Multiphase Flow
• A blow-up criterion for compressible viscous heat-conductive flows
• A blow-up criterion for compressible viscous heat-conductive flows

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