Existence of Strong Solutions for Electrorheological Fluids in Two Dimensions: Steady Dirichlet Problem

2003 ◽  
pp. 591-602 ◽  
Author(s):  
Frank Ettwein ◽  
Michael Růžička
Keyword(s):  
Dirichlet Problem ◽  
Strong Solutions ◽  
Two Dimensions ◽  
Electrorheological Fluids

scholarly journals C1,α-regularity for electrorheological fluids in two dimensions

2007 ◽  
Vol 14 (1-2) ◽  
pp. 207-217 ◽  
Author(s):  
L. Diening ◽  
F. Ettwein ◽  
M. Růžička
Keyword(s):  
Two Dimensions ◽  
Electrorheological Fluids

scholarly journals Well-Posedness of Strong Solutions to the Anelastic Equations of Stratified Viscous Flows

2020 ◽  
Vol 22 (3) ◽  
Author(s):  
Xin Liu ◽  
Edriss S. Titi
Keyword(s):  
Initial Data ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Viscous Flows ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Physical Vacuum ◽  
Well Posedness ◽  
Small Initial Data ◽  
Anelastic Equations

Abstract We establish the local and global well-posedness of strong solutions to the two- and three-dimensional anelastic equations of stratified viscous flows. In this model, the interaction of the density profile with the velocity field is taken into account, and the density background profile is permitted to have physical vacuum singularity. The existing time of the solutions is infinite in two dimensions, with general initial data, and in three dimensions with small initial data.

scholarly journals Analysis of a mixture model of tumor growth

2013 ◽  
Vol 24 (5) ◽  
pp. 691-734 ◽  
Author(s):  
JOHN LOWENGRUB ◽  
EDRISS TITI ◽  
KUN ZHAO
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Strong Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Finite Energy ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Spatial Regularity ◽  
Initial Boundary Value

We study an initial-boundary value problem for a coupled Cahn–Hilliard–Hele–Shaw system that models tumour growth. For large initial data with finite energy, we prove global (local resp.) existence, uniqueness, higher order spatial regularity and the Gevrey spatial regularity of strong solutions to the initial-boundary value problem in two dimensions (three dimensions resp.). Asymptotically in time, we show that the solution converges to a constant state exponentially fast as time tends to infinity under certain assumptions.

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