Mathematical properties of the Navier-Stokes dynamical system for incompressible Newtonian fluids

@article{50307,
   author = {Cremaschini, Claudio and Tessarotto, Massimo},
   article_location = {NL - Nizozemsko},
   article_number = {18},
   doi = {http://dx.doi.org/10.1016/j.physa.2013.04.054},
   keywords = {Navier-Stokes equations; Dynamical systems; Kinetic theory; Existence theorem},
   issn = {0378-4371},
   journal = {PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS},
   title = {Mathematical properties of the Navier-Stokes dynamical system for incompressible Newtonian fluids},
   url = {https://www.sciencedirect.com/science/article/abs/pii/S0378437113003853},
   volume = {392},
   year = {2013}
}

TY  - JOUR
ID  - 50307
AU  - Cremaschini, Claudio - Tessarotto, Massimo
PY  - 2013
TI  - Mathematical properties of the Navier-Stokes dynamical system for incompressible Newtonian fluids
JF  - PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
VL  - 392
IS  - 18
SN  - 03784371
KW  - Navier-Stokes equations
KW  - Dynamical systems
KW  - Kinetic theory
KW  - Existence theorem
UR  - https://www.sciencedirect.com/science/article/abs/pii/S0378437113003853
N2  - The connection between fluid dynamics and classical statistical mechanics has motivated in the past mathematical investigations of the incompressible Navier-Stokes (NS) equations (INSE) by means of an asymptotic kinetic theory. This feature has suggestedthe search for possible alternative exact approaches, based on the construction of a suitable inverse kinetic theory (IKT), which can avoid the asymptotic character and the intrinsic mathematical difficulty of direct kinetic theories. In this paper thefundamental mathematical properties of the NS phase-space dynamical system underlying INSE and determined by IKT are investigated. In particular, an equivalence theorem with the INSE problem and a global existence theorem are proved to hold for the NS dynamical system.
ER  - 

CREMASCHINI, Claudio a Massimo TESSAROTTO. Mathematical properties of the Navier-Stokes dynamical system for incompressible Newtonian fluids. \textit{PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS}. NL - Nizozemsko, 2013, roč.~392, č.~18, 7 s. ISSN~0378-4371. Dostupné z: https://dx.doi.org/10.1016/j.physa.2013.04.054.