Weak Solutions for an Incompressible Newtonian Fluid Interacting with a Koiter Type Shell

2013 ◽  
Vol 211 (1) ◽  
pp. 205-255 ◽  
Author(s):  
Daniel Lengeler ◽  
Michael Růžička
Keyword(s):  
Newtonian Fluid ◽  
Weak Solutions ◽  
Incompressible Newtonian Fluid

scholarly journals On a degenerate parabolic equation with Newtonian fluid∼non-Newtonian fluid mixed type

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sujun Weng
Keyword(s):  
Parabolic Equation ◽  
Newtonian Fluid ◽  
Weak Solutions ◽  
Mixed Type ◽  
Degenerate Parabolic Equation ◽  
Type Equation ◽  
Existence Of Weak Solutions ◽  
Degenerate Parabolic ◽  
The Stability ◽  
Increasing Function

AbstractWe study the existence of weak solutions to a Newtonian fluid∼non-Newtonian fluid mixed-type equation $$ {u_{t}}= \operatorname{div} \bigl(b(x,t){ \bigl\vert {\nabla A(u)} \bigr\vert ^{p(x) - 2}}\nabla A(u)+\alpha (x,t)\nabla A(u) \bigr)+f(u,x,t). $$ u t = div ( b ( x , t ) | ∇ A ( u ) | p ( x ) − 2 ∇ A ( u ) + α ( x , t ) ∇ A ( u ) ) + f ( u , x , t ) . We assume that $A'(s)=a(s)\geq 0$ A ′ ( s ) = a ( s ) ≥ 0 , $A(s)$ A ( s ) is a strictly increasing function, $A(0)=0$ A ( 0 ) = 0 , $b(x,t)\geq 0$ b ( x , t ) ≥ 0 , and $\alpha (x,t)\geq 0$ α ( x , t ) ≥ 0 . If $$ b(x,t)=\alpha (x,t)=0,\quad (x,t)\in \partial \Omega \times [0,T], $$ b ( x , t ) = α ( x , t ) = 0 , ( x , t ) ∈ ∂ Ω × [ 0 , T ] , then we prove the stability of weak solutions without the boundary value condition.

scholarly journals A Hybrid Approach for the Simulation of the Thermal Motion of a Nearly Neutrally Buoyant Nanoparticle in an Incompressible Newtonian Fluid Medium

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
B. Uma ◽  
R. Radhakrishnan ◽  
D. M. Eckmann ◽  
P. S. Ayyaswamy
Keyword(s):  
Newtonian Fluid ◽  
Brownian Particle ◽  
Equations Of Motion ◽  
Hybrid Approach ◽  
Thermal Motion ◽  
Fluctuating Hydrodynamics ◽  
Arbitrary Lagrangian Eulerian ◽  
Fluid Medium ◽  
Incompressible Newtonian Fluid ◽  
Neutrally Buoyant

A hybrid approach consisting of a Markovian fluctuating hydrodynamics of the fluid and a non-Markovian Langevin dynamics with the Ornstein–Uhlenbeck noise perturbing the translational and rotational equations of motion of a nanoparticle is employed to study the thermal motion of a nearly neutrally buoyant nanoparticle in an incompressible Newtonian fluid medium. A direct numerical simulation adopting an arbitrary Lagrangian–Eulerian based finite element method is employed for the simulation of the hybrid approach. The instantaneous flow around the particle and the particle motion are fully resolved. The numerical results show that (a) the calculated temperature of the nearly neutrally buoyant Brownian particle in a quiescent fluid satisfies the equipartition theorem; (b) the translational and rotational decay of the velocity autocorrelation functions result in algebraic tails, over long time; (c) the translational and rotational mean square displacements of the particle obey Stokes–Einstein and Stokes–Einstein–Debye relations, respectively; and (d) the parallel and perpendicular diffusivities of the particle closer to the wall are consistent with the analytical results, where available. The study has important implications for designing nanocarriers for targeted drug delivery. A major advantage of our novel hybrid approach employed in this paper as compared to either the fluctuating hydrodynamics approach or the generalized Langevin approach by itself is that only the hybrid method has been shown to simultaneously preserve both hydrodynamic correlations and equilibrium statistics in the incompressible limit.

scholarly journals Experimental realization of an incompressible Newtonian fluid in two dimensions

2016 ◽  
Vol 93 (1) ◽  
Author(s):  
Zhiyuan Qi ◽  
Cheol Soo Park ◽  
Matthew A. Glaser ◽  
Joseph E. Maclennan ◽  
Noel A. Clark
Keyword(s):  
Newtonian Fluid ◽  
Two Dimensions ◽  
Experimental Realization ◽  
Incompressible Newtonian Fluid

scholarly journals On the uniqueness for weak solutions of steady double-phase fluids

2021 ◽  
Vol 11 (1) ◽  
pp. 454-468
Author(s):  
Mohamed Abdelwahed ◽  
Luigi C. Berselli ◽  
Nejmeddine Chorfi
Keyword(s):  
Stress Tensor ◽  
Newtonian Fluid ◽  
Weak Solutions ◽  
Convective Term ◽  
Anisotropic Stress ◽  
Stress Tensors ◽  
Double Phase ◽  
Wide Range

Abstract We consider a double-phase non-Newtonian fluid, described by a stress tensor which is the sum of a p-Stokes and a q-Stokes stress tensor, with 1 < p<2 < q<∞. For a wide range of parameters (p, q), we prove the uniqueness of small solutions. We use the p < 2 features to obtain quadratic-type estimates for the stress-tensor, while we use the improved regularity coming from the term with q > 2 to justify calculations for weak solutions. Results are obtained through a careful use of the symmetries of the convective term and are also valid for rather general (even anisotropic) stress-tensors.

An equation of motion for an incompressible Newtonian fluid in a packed bed

1995 ◽  
Vol 18 (2) ◽  
pp. 185-198 ◽  
Author(s):  
R. E. Hayes ◽  
A. Afacan ◽  
B. Boulanger
Keyword(s):  
Newtonian Fluid ◽  
Packed Bed ◽  
Equation Of Motion ◽  
Incompressible Newtonian Fluid
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