A parabolic system involving a quadratic gradient term related to the Boussinesq approximation.

Díaz, Jesús Ildefonso, Rakotoson, Jean-Michel, and Schmidt, Paul G.. "A parabolic system involving a quadratic gradient term related to the Boussinesq approximation.." RACSAM 101.1 (2007): 113-118. <http://eudml.org/doc/41669>.

@article{Díaz2007,
abstract = {We propose a modification of the classical Boussinesq approximation for buoyancy-driven flows of viscous, incompressible fluids in situations where viscous heating cannot be neglected. This modification is motivated by unresolved issues regarding the global solvability of the original system. A very simple model problem leads to a coupled system of two parabolic equations with a source term involving the square of the gradient of one of the unknowns. Based on adequate notions of weak and strong solutions, we establish the global-in-time existence of weak solutions and the uniqueness of strong solutions.},
author = {Díaz, Jesús Ildefonso, Rakotoson, Jean-Michel, Schmidt, Paul G.},
journal = {RACSAM},
keywords = {Boussinesq approximation; parabolic system; buoyancy-driven flows},
language = {eng},
number = {1},
pages = {113-118},
title = {A parabolic system involving a quadratic gradient term related to the Boussinesq approximation.},
url = {http://eudml.org/doc/41669},
volume = {101},
year = {2007},
}

TY - JOUR
AU - Díaz, Jesús Ildefonso
AU - Rakotoson, Jean-Michel
AU - Schmidt, Paul G.
TI - A parabolic system involving a quadratic gradient term related to the Boussinesq approximation.
JO - RACSAM
PY - 2007
VL - 101
IS - 1
SP - 113
EP - 118
AB - We propose a modification of the classical Boussinesq approximation for buoyancy-driven flows of viscous, incompressible fluids in situations where viscous heating cannot be neglected. This modification is motivated by unresolved issues regarding the global solvability of the original system. A very simple model problem leads to a coupled system of two parabolic equations with a source term involving the square of the gradient of one of the unknowns. Based on adequate notions of weak and strong solutions, we establish the global-in-time existence of weak solutions and the uniqueness of strong solutions.
LA - eng
KW - Boussinesq approximation; parabolic system; buoyancy-driven flows
UR - http://eudml.org/doc/41669
ER -