Well‐posedness for the FENE dumbbell model of polymeric flows

By Nader Masmoudi. 2008

137 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/02107645674cdc2fb52aafd5a3251d4a0e88c8d3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Nader Masmoudi
2. Peter Constantin
3. Markus Kliegl
4. Marius Paicu
5. Zhen Lei
6. Arghir Zarnescu
7. Yi Zhou
8. Juhi Jang

In Computational Mechanics

1. Peter Constantin
2. Nader Masmoudi
3. Marius Paicu
4. Markus Kliegl
5. Arghir Zarnescu
6. Zhen Lei
7. Juhi Jang
8. Yi Zhou

In Mathematical Physics

1. Nader Masmoudi
2. Marius Paicu
3. Arghir Zarnescu
4. Zhen Lei
5. Peter Constantin
6. Markus Kliegl
7. Juhi Jang
8. Yi Zhou

Citations in the corpus

• Global existence of weak solutions to macroscopic models of polymeric flows (2011, background): “Local well-posedness was also proved in [40] when b = 2k > 0 (see also [25]).”
• About the Hardy Inequality (2011, background): “These include equations describing thin films or porous media [1], or so-called “Fokker-Planck equations” for polymers [ 9 ].”
• Note on Global Regularity for Two-Dimensional Oldroyd-B Fluids with Diffusive Stress (2012, methodology): “For the FENE equations (see [2] for numerical results and set-up) ([27]) proves local well-posedness in general, and global well posedness for the corotational case.”
• Global existence of weak solutions to some micro-macro models (2007, unknown): “We do not detail the proof here (see [11]).”
• Global well posedness for the Maxwell-Navier-Stokes system in 2D (2010, methodology): “This estimate (and similar ones) were used extensively in many mathematical results about Oldroyd B model and polymeric flows in 2D (see [27,10,26,21,19]).”
• Energy Dissipation and Regularity for a Coupled Navier–Stokes and Q-Tensor System (2010, methodology): “The system we study is related structurally to other models of complex fluids coupling a transport equation with a forced Navier-Stokes system [1], [6], [7], [8], [10], [17], [18], [22], [26].”
• Well‐posedness of Compressible Euler Equations in a Physical Vacuum (2010, background): “Also, similar problems arise in degenerate parabolic equations, for instance, in porous medium equations [7], in thin film equations [20], and in the study of polymeric flows [55].”
• Remarks on the blowup criteria for Oldroyd models (2009, background): “3), the authors in [5] use a losing a priori estimate for solutions of transport equations which was developed by Bahouri and Chemin [1] and used later on by a lot of authors (for example, see [6, 5, 7, 16, 21, 18, 19] and the references therein).”