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Incompressible Limit of isentropic Navier-Stokes equations with Navier-slip boundary
Institute of Mathematics, Hunan University, Changsha 410082, China |
This paper concerns the low Mach number limit of weak solutions to the compressible Navier-Stokes equations for isentropic fluids in a bounded domain with a Navier-slip boundary condition. In [
References:
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B. Desjardins and E. Grenier,
Low Mach number limit of viscous compressible flows in the whole space, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 455 (1999), 2271-2279.
doi: 10.1098/rspa.1999.0403. |
[2] |
B. Desjardins, E. Grenier, P.-L. Lions and N. Masmoudi,
Incompressible limit for a viscous compressible fluid, J. Math. Pures Appl. (9), 78 (1999), 461-471.
doi: 10.1016/S0021-7824(98)80139-6. |
[3] |
E. Feireisl, A. Novotný and H. Petzeltová,
On the existence of globally defined weak solutions to the Navier-Stokes equations, J. Math. Fluid Mech., 3 (2001), 358-392.
doi: 10.1007/PL00000976. |
[4] |
E. Grenier,
Oscillatory perturbations of the Navier-Stokes equations, J. Math. Pures Appl. (9), 76 (1997), 477-498.
doi: 10.1016/S0021-7824(97)89959-X. |
[5] |
N. Jiang and N. Masmoudi,
On the construction of boundary layers in the incompressible limit with boundary, J. Math. Pures Appl. (9), 103 (2015), 269-290.
doi: 10.1016/j.matpur.2014.04.004. |
[6] |
N. Jiang and N. Masmoudi,
Boundary layers and incompressible Navier-Stokes-Fourier limit of the Boltzmann equation in bounded domain I, Comm. Pure Appl. Math., 70 (2017), 90-171.
doi: 10.1002/cpa.21631. |
[7] |
P.-L. Lions and N. Masmoudi,
Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions, J. Math. Pures Appl. (9), 77 (1998), 585-627.
doi: 10.1016/S0021-7824(98)80139-6. |
[8] |
P. -L. Lions,
Mathematical Topics in Fluid Mechanics. Vol. 1: Incompressible Models, The Clarendon Press, Oxford University Press, New York, 1996. |
[9] |
P. -L. Lions,
Mathematical Topics in Fluid Mechanics. Vol. 2: Compressible Models, The Clarendon Press, Oxford University Press, New York, 1998. |
[10] |
S. Schochet,
Fast singular limits of hyperbolic PDEs, J. Differential Equations, 114 (1994), 476-512.
doi: 10.1006/jdeq.1994.1157. |
[11] |
L. Simon,
Theorems on Regularity and Singularity of Energy Minimizing Maps, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 1996. |
show all references
References:
[1] |
B. Desjardins and E. Grenier,
Low Mach number limit of viscous compressible flows in the whole space, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 455 (1999), 2271-2279.
doi: 10.1098/rspa.1999.0403. |
[2] |
B. Desjardins, E. Grenier, P.-L. Lions and N. Masmoudi,
Incompressible limit for a viscous compressible fluid, J. Math. Pures Appl. (9), 78 (1999), 461-471.
doi: 10.1016/S0021-7824(98)80139-6. |
[3] |
E. Feireisl, A. Novotný and H. Petzeltová,
On the existence of globally defined weak solutions to the Navier-Stokes equations, J. Math. Fluid Mech., 3 (2001), 358-392.
doi: 10.1007/PL00000976. |
[4] |
E. Grenier,
Oscillatory perturbations of the Navier-Stokes equations, J. Math. Pures Appl. (9), 76 (1997), 477-498.
doi: 10.1016/S0021-7824(97)89959-X. |
[5] |
N. Jiang and N. Masmoudi,
On the construction of boundary layers in the incompressible limit with boundary, J. Math. Pures Appl. (9), 103 (2015), 269-290.
doi: 10.1016/j.matpur.2014.04.004. |
[6] |
N. Jiang and N. Masmoudi,
Boundary layers and incompressible Navier-Stokes-Fourier limit of the Boltzmann equation in bounded domain I, Comm. Pure Appl. Math., 70 (2017), 90-171.
doi: 10.1002/cpa.21631. |
[7] |
P.-L. Lions and N. Masmoudi,
Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions, J. Math. Pures Appl. (9), 77 (1998), 585-627.
doi: 10.1016/S0021-7824(98)80139-6. |
[8] |
P. -L. Lions,
Mathematical Topics in Fluid Mechanics. Vol. 1: Incompressible Models, The Clarendon Press, Oxford University Press, New York, 1996. |
[9] |
P. -L. Lions,
Mathematical Topics in Fluid Mechanics. Vol. 2: Compressible Models, The Clarendon Press, Oxford University Press, New York, 1998. |
[10] |
S. Schochet,
Fast singular limits of hyperbolic PDEs, J. Differential Equations, 114 (1994), 476-512.
doi: 10.1006/jdeq.1994.1157. |
[11] |
L. Simon,
Theorems on Regularity and Singularity of Energy Minimizing Maps, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 1996. |
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