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A challenging open problem: The inviscid limit under slip-type boundary conditions.
A representation formula for linearized stationary incompressible viscous flows around rotating and translating bodies
| 1. | Univ Lille Nord de France, 59000 Lille, France |
| 2. | Department of Technical Mathematics, Czech Technical University, Karlovo nám. 13, 121 35 Prague 2, Czech Republic |
| 3. | Mathematical Institute of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Prague 1 |
| [1] |
Reinhard Farwig, Ronald B. Guenther, Enrique A. Thomann, Šárka Nečasová. The fundamental solution of linearized nonstationary Navier-Stokes equations of motion around a rotating and translating body. Discrete & Continuous Dynamical Systems - A, 2014, 34 (2) : 511-529. doi: 10.3934/dcds.2014.34.511 |
| [2] |
Paul Deuring, Stanislav Kračmar, Šárka Nečasová. A leading term for the velocity of stationary viscous incompressible flow around a rigid body performing a rotation and a translation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (3) : 1389-1409. doi: 10.3934/dcds.2017057 |
| [3] |
Paul Deuring, Stanislav Kračmar, Šárka Nečasová. A linearized system describing stationary incompressible viscous flow around rotating and translating bodies: Improved decay estimates of the velocity and its gradient. Conference Publications, 2011, 2011 (Special) : 351-361. doi: 10.3934/proc.2011.2011.351 |
| [4] |
Paul Deuring, Stanislav Kračmar, Šárka Nečasová. Linearized stationary incompressible flow around rotating and translating bodies -- Leray solutions. Discrete & Continuous Dynamical Systems - S, 2014, 7 (5) : 967-979. doi: 10.3934/dcdss.2014.7.967 |
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Hua Qiu. Regularity criteria of smooth solution to the incompressible viscoelastic flow. Communications on Pure & Applied Analysis, 2013, 12 (6) : 2873-2888. doi: 10.3934/cpaa.2013.12.2873 |
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Quan Wang. Stability and bifurcation of a viscous incompressible plasma fluid contained between two concentric rotating cylinders. Discrete & Continuous Dynamical Systems - B, 2014, 19 (2) : 543-563. doi: 10.3934/dcdsb.2014.19.543 |
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Doretta Vivona, Pierre Capodanno. Mathematical study of the small oscillations of a floating body in a bounded tank containing an incompressible viscous liquid. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 2353-2364. doi: 10.3934/dcdsb.2014.19.2353 |
| [8] |
Xiaoli Li. Global strong solution for the incompressible flow of liquid crystals with vacuum in dimension two. Discrete & Continuous Dynamical Systems - A, 2017, 37 (9) : 4907-4922. doi: 10.3934/dcds.2017211 |
| [9] |
Hua Qiu, Shaomei Fang. A BKM's criterion of smooth solution to the incompressible viscoelastic flow. Communications on Pure & Applied Analysis, 2014, 13 (2) : 823-833. doi: 10.3934/cpaa.2014.13.823 |
| [10] |
Baoquan Yuan. Note on the blowup criterion of smooth solution to the incompressible viscoelastic flow. Discrete & Continuous Dynamical Systems - A, 2013, 33 (5) : 2211-2219. doi: 10.3934/dcds.2013.33.2211 |
| [11] |
Jiří Neustupa. On $L^2$-Boundedness of a $C_0$-Semigroup generated by the perturbed oseen-type operator arising from flow around a rotating body. Conference Publications, 2007, 2007 (Special) : 758-767. doi: 10.3934/proc.2007.2007.758 |
| [12] |
Juliana Honda Lopes, Gabriela Planas. Well-posedness for a non-isothermal flow of two viscous incompressible fluids. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2455-2477. doi: 10.3934/cpaa.2018117 |
| [13] |
Matthieu Hillairet, Ayman Moussa, Franck Sueur. On the effect of polydispersity and rotation on the Brinkman force induced by a cloud of particles on a viscous incompressible flow. Kinetic & Related Models, 2019, 12 (4) : 681-701. doi: 10.3934/krm.2019026 |
| [14] |
Luisa Fermo, Andrea Tosin. Fundamental diagrams for kinetic equations of traffic flow. Discrete & Continuous Dynamical Systems - S, 2014, 7 (3) : 449-462. doi: 10.3934/dcdss.2014.7.449 |
| [15] |
Giancarlo Benettin, Anna Maria Cherubini, Francesco Fassò. Regular and chaotic motions of the fast rotating rigid body: a numerical study. Discrete & Continuous Dynamical Systems - B, 2002, 2 (4) : 521-540. doi: 10.3934/dcdsb.2002.2.521 |
| [16] |
Manh Hong Duong, Hoang Minh Tran. On the fundamental solution and a variational formulation for a degenerate diffusion of Kolmogorov type. Discrete & Continuous Dynamical Systems - A, 2018, 38 (7) : 3407-3438. doi: 10.3934/dcds.2018146 |
| [17] |
Boling Guo, Guangwu Wang. Existence of the solution for the viscous bipolar quantum hydrodynamic model. Discrete & Continuous Dynamical Systems - A, 2017, 37 (6) : 3183-3210. doi: 10.3934/dcds.2017136 |
| [18] |
Fei Jiang, Song Jiang, Weiwei Wang. Nonlinear Rayleigh-Taylor instability for nonhomogeneous incompressible viscous magnetohydrodynamic flows. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 1853-1898. doi: 10.3934/dcdss.2016076 |
| [19] |
Gui-Qiang Chen, Bo Su. A viscous approximation for a multidimensional unsteady Euler flow: Existence theorem for potential flow. Discrete & Continuous Dynamical Systems - A, 2003, 9 (6) : 1587-1606. doi: 10.3934/dcds.2003.9.1587 |
| [20] |
Bendong Lou. Spiral rotating waves of a geodesic curvature flow on the unit sphere. Discrete & Continuous Dynamical Systems - B, 2012, 17 (3) : 933-942. doi: 10.3934/dcdsb.2012.17.933 |
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