# On weak solutions to the equations of non-stationary motion of heat-conducting incompressible viscous fluids: defect measure and energy equality

Banach Center Publications (2008)

- Volume: 81, Issue: 1, page 287-296
- ISSN: 0137-6934

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topJoachim Naumann. "On weak solutions to the equations of non-stationary motion of heat-conducting incompressible viscous fluids: defect measure and energy equality." Banach Center Publications 81.1 (2008): 287-296. <http://eudml.org/doc/282393>.

@article{JoachimNaumann2008,

abstract = {We consider the non-stationary Navier-Stokes equations completed by the equation of conservation of internal energy. The viscosity of the fluid is assumed to depend on the temperature, and the dissipation term is the only heat source in the conservation of internal energy. For the system of PDE's under consideration, we prove the existence of a weak solution such that: 1) the weak form of the conservation of internal energy involves a defect measure, and 2) the equality for the total energy is satisfied.},

author = {Joachim Naumann},

journal = {Banach Center Publications},

keywords = {Navier-Stokes equations; existence of weak solutions},

language = {eng},

number = {1},

pages = {287-296},

title = {On weak solutions to the equations of non-stationary motion of heat-conducting incompressible viscous fluids: defect measure and energy equality},

url = {http://eudml.org/doc/282393},

volume = {81},

year = {2008},

}

TY - JOUR

AU - Joachim Naumann

TI - On weak solutions to the equations of non-stationary motion of heat-conducting incompressible viscous fluids: defect measure and energy equality

JO - Banach Center Publications

PY - 2008

VL - 81

IS - 1

SP - 287

EP - 296

AB - We consider the non-stationary Navier-Stokes equations completed by the equation of conservation of internal energy. The viscosity of the fluid is assumed to depend on the temperature, and the dissipation term is the only heat source in the conservation of internal energy. For the system of PDE's under consideration, we prove the existence of a weak solution such that: 1) the weak form of the conservation of internal energy involves a defect measure, and 2) the equality for the total energy is satisfied.

LA - eng

KW - Navier-Stokes equations; existence of weak solutions

UR - http://eudml.org/doc/282393

ER -

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