About Lifespan of Regular Solutions of Equations Related to Viscoelastic Fluids

By Jean-Yves Chemin, Nader Masmoudi. SIAM Journal on Mathematical Analysis, 2001

321 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/c50aee49063e7d6079dc7ffa48aedfe3f703b7f4

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In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Estimates in Besov spaces for transport and transport-diffusion equations with almost Lipschitz coefficients (2005, unknown): “Linear loss of regularity In this part, we aim at extending the results [1] and [6] to general Besov spaces.”
Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations (2013, methodology): “The multiplier J replaces growth in time by controlled loss of regularity and is reminiscent of the notion of losing regularity estimates used in [3, 25].”
Global Well-Posedness for Compressible Viscoelastic Fluids near Equilibrium (2010, background): “is the Cauchy‐Green strain tensor, Chemin and Masmoudi [ 3 ] proved the existence of a local solution and a global small solution in critical Besov spaces.”
LOCAL THEORY IN CRITICAL SPACES FOR COMPRESSIBLE VISCOUS AND HEAT-CONDUCTIVE GASES (2001, background): “Let us mention that similar spaces have been used in [7] to investigate equations related to viscoelastic fluids, and in a joint work with B.”
Global existence of weak solutions to some micro-macro models (2007, unknown): “If R is in the whole space, the model reduces to the Hooke model for which φ(R) = k|R| and the model reduces to the Oldroyd-B model (see [3] and [10] for some local and global existence results).”
Note on Global Regularity for Two-Dimensional Oldroyd-B Fluids with Diffusive Stress (2012, background): “Sufficient conditions for regularity in terms of bounds on the added stress tensor were established in ([3], [17]) and further refined in ([20]).”
Energy Dissipation and Regularity for a Coupled Navier–Stokes and Q-Tensor System (2010, methodology): “([9],[10]) (i) (Bernstein inequalities) 2‖∇Squ‖Lp ≤ C‖u‖Lp, ∀1 ≤ p ≤ ∞ ‖∆qu‖Lp ≤ C2 ‖∆q∇u‖Lp ≤ C‖∆qu‖Lp , ∀1 ≤ p ≤ ∞ (ii)(commutator estimate) ‖[Sq′−1a,∆q]b‖L2 ≤ C2 ‖∇Sq′−1a‖L∞‖b‖L2”
GLOBAL SOLUTIONS FOR SOME OLDROYD MODELS OF NON-NEWTONIAN FLOWS (2000, methodology): “For more details on the macroscopic models, we refer the reader to [11, 2] (for instance) while information on the so-called micro-macro models can be found in [3, 10, 19, 20, · · · ].”
The Global Existence of Small Solutions to the Incompressible Viscoelastic Fluid System in 2 and 3 Space Dimensions (2006, background): “We should point out that when one add a damping term in the evolution equation of UU T , which is the Cauchy–Green strain tensor, Chemin and Masmoudi ( 2001 ) established the global well-posedness for this modified system.”
Well‐posedness for the FENE dumbbell model of polymeric flows (2008, methodology): “[6] J.-Y. Chemin and N. Masmoudi.”
Global well posedness for the Maxwell-Navier-Stokes system in 2D (2010, result): “We refer to [7,9] for the proof of the following results and for the multiplication law in Besov spaces.”