Classical solutions to one-dimensional stationary quantum Navier-Stokes equations

DOI10.1016/J.MATPUR.2011.07.005zbMath1239.35108OpenAlexW2000863553MaRDI QIDQ650848

Jian-Wei Dong

Publication date: 7 December 2011

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.2011.07.005

zbMATH Keywords

stationary solutionsLeray-Schauder fixed-point theoremquantum Navier-Stokes equationviscous quantum Euler equation

Mathematics Subject Classification ID

Navier-Stokes equations (35Q30) PDEs in connection with quantum mechanics (35Q40) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Euler equations (35Q31)

Related Items (4)

Exponential decay in time of density of one-dimensional quantum Navier-Stokes equations ⋮ Existence of classical solutions to a stationary simplified quantum energy-transport model in 1-dimensional space ⋮ On the blowing up of solutions to one-dimensional quantum Navier-Stokes equations ⋮ Remarks on classical solutions to steady quantum Navier-Stokes equations

Cites Work

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• Effective velocity in compressible Navier-Stokes equations with third-order derivatives
• A remark on weak solutions to the barotropic compressible quantum Navier-Stokes equations
• On the construction of approximate solutions for the 2D viscous shallow water model and for compressible Navier-Stokes models
• On compressible Navier-Stokes equations with density dependent viscosities in bounded domains
• On the existence of global weak solutions to the Navier-Stokes equations for viscous compressible and heat conducting fluids
• A note on barotropic compressible quantum Navier-Stokes equations
• Vanishing of vacuum states and blow-up phenomena of the compressible Navier-Stokes equations
• On the Barotropic Compressible Navier–Stokes Equations
• Global Weak Solutions to Compressible Navier–Stokes Equations for Quantum Fluids

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