TY - JOUR
T1 - Analysis of a Navier–Stokes phase-field crystal system
AU - Cavaterra, Cecilia
AU - Grasselli, Maurizio
AU - Mehmood, Muhammed Ali
AU - Voso, Riccardo
N1 - Publisher Copyright:
© 2024
PY - 2024/11/22
Y1 - 2024/11/22
N2 - We consider an evolution system modeling a flow of colloidal particles which are suspended in an incompressible fluid and accounts for colloidal crystallization. The system consists of the Navier–Stokes equations for the volume averaged velocity coupled with the so-called Phase-Field Crystal equation for the density deviation. Considering this system in a periodic domain and assuming that the viscosity as well as the mobility depend on the density deviation, we first prove the existence of a weak solution in dimension three. Then, in dimension two, we establish the existence of a (unique) strong solution.
AB - We consider an evolution system modeling a flow of colloidal particles which are suspended in an incompressible fluid and accounts for colloidal crystallization. The system consists of the Navier–Stokes equations for the volume averaged velocity coupled with the so-called Phase-Field Crystal equation for the density deviation. Considering this system in a periodic domain and assuming that the viscosity as well as the mobility depend on the density deviation, we first prove the existence of a weak solution in dimension three. Then, in dimension two, we establish the existence of a (unique) strong solution.
KW - Navier–Stokes system
KW - Phase-field crystal equation
KW - Strong solutions
KW - Weak solutions
UR - http://www.scopus.com/inward/record.url?scp=85209638386&partnerID=8YFLogxK
U2 - 10.1016/j.nonrwa.2024.104263
DO - 10.1016/j.nonrwa.2024.104263
M3 - Article
SN - 1468-1218
VL - 83
JO - Nonlinear Analysis: Real World Applications
JF - Nonlinear Analysis: Real World Applications
M1 - 104263
ER -