Theoretical study of a Bénard-Marangoni problem

DOI10.1016/j.jmaa.2010.10.064zbMath1208.35115OpenAlexW1979386781MaRDI QIDQ624578

Sergio Hoyas, Henar Herrero, Rosa Pardo San Gil

Publication date: 9 February 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2010.10.064

zbMATH Keywords

bifurcationthermal convectionfluid dynamicsBénard-Marangoni problemincompressible Boussinesq-Navier-Stokes equations

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Capillarity (surface tension) for incompressible viscous fluids (76D45) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Forced convection (76R05) Bifurcations in context of PDEs (35B32)

Related Items

A time-dependent perturbation solution from a steady state for Marangoni problem, On the Rayleigh-Bénard-Marangoni system and a related optimal control problem, On the Rayleigh-Bénard-Marangoni problem: theoretical and numerical analysis

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mixed boundary value problems for the stationary Navier-Stokes system in polyhedral domains
• Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
• Stationary solutions for generalized Boussinesq models
• Singular behavior of elliptic problems in non Hilbertian Sobolev spaces
• The Boussinesq system with mixed nonsmooth boundary data
• Existence and nonuniqueness of rectangular solutions of the Benard problem
• Some global results for nonlinear eigenvalue problems
• Bifurcation from simple eigenvalues
• On convection cells induced by surface tension
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Instabilities of dynamic thermocapillary liquid layers. Part 2. Surface-wave instabilities
• Some optimal control problems of multistate equations appearing in fluid mechanics
• The initial value problem for a generalized Boussinesq model
• Bénard–Marangoni instability in rigid rectangular containers
• Thermal convection in a cylindrical annulus heated laterally
• On the existence and uniqueness of the stationary solution to equations of natural convection with boundary data in L ²
• Lp estimates of solutions tomixed boundary value problems for the Stokes system in polyhedral domains
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II