On hydrodynamics of viscoelastic fluids

By F. Lin, Chun Liu, Ping Zhang. 2005

435 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fbc0a86a8b30c4fb9faae2951bafc373dc998dae

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Global Solutions for Incompressible Viscoelastic Fluids (2008, methodology): “It is worth noticing that they used an Eulerian description of the problem, which is equivalent to that in [27, 25].”
The Global Existence of Small Solutions to the Incompressible Viscoelastic Fluid System in 2 and 3 Space Dimensions (2006, methodology): “Actually one may obtain a much more complex system than (1.1) if one persists to find such kind of equivalent form (see Lin et al., 2005).”
Energy Dissipation and Regularity for a Coupled Navier–Stokes and Q-Tensor System (2010, methodology): “The system we study is structurally related to other models of complex fluids coupling a transport equation with a forced Navier–Stokes system [2,7–10,14,18,20,22,25,27].”
Global Existence for the Multi-Dimensional Compressible Viscoelastic flows (2010, background): “1) is concerned with the curl of the deformation gradient (for the incompressible case, see [13, 16]).”
Global existence of weak solutions to some micro-macro models (2007, neutral): “We can mention Jourdain, Lelievre and Le Bris [8], Weinan E, Li and Zhang [7] and Zhang and Zhang [14], Lin, Liu and Zhang [9] and Barrett, Schwab and Suli [1].”
Global Well-Posedness for Compressible Viscoelastic Fluids near Equilibrium (2010, methodology): “There have been many attempts to capture different phenomena for non-Newtonian fluids, see [11,12,14,18,21].”
Well‐posedness for the FENE dumbbell model of polymeric flows (2008, methodology): “[24] F.-H. Lin, C. Liu, and P. Zhang.”
On the initial‐boundary value problem of the incompressible viscoelastic fluid system (2008, methodology): “1) (see also [11, 14] for more details).”
GLOBAL WELL-POSEDNESS OF THE VISCOUS BOUSSINESQ EQUATIONS (2004, result): “We should also mention the recent work of Lin, Liu, and Zhang [12] who establish the local existence and global existence (with small initial data) of classical solutions for an Oldroyd-system in which viscosity enters only in the fluid equation, but not in the elasticity equation.”
Global Regularity for Some Oldroyd‐B Type Models (2013, positive): “Many works have been devoted to the proof of global well-posedness in the case of small data after the work of F.H. Lin et al. ([19], [20], [21]).”
On the Euler equations of incompressible fluids (2007, background): “The well-posedness theory is difficult even in two space dimensions, and consequently the mathematical theory of complex fluids is in its developing stages ([43], [48], [52], [76], [89], [98], [100], [101], [103], [115]).”
Note on Global Regularity for Two-Dimensional Oldroyd-B Fluids with Diffusive Stress (2012, methodology): “An approach based on Lagrangian particle dynamics was developed in ([22]).”
Global Small Solutions to an MHD‐Type System: The Three‐Dimensional Case (2014, methodology): “The authors [13] established the global existence of smooth solutions to the Cauchy problem in the entire space or on a periodic domain for (1.”
Global existence of weak solutions to macroscopic models of polymeric flows (2011, methodology): “E, Li and Zhang [13] proved local existence when R is taken in the whole space and under some growth condition on the potential.”