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Linearized Navier-Stokes equations in $\mathbb{R}^3$: An approach in weighted Sobolev spaces
Global strong solution to the initial-boundary value problem of a 2-D Kazhikhov-Smagulov type model
1. | Department of Mathematics, Nanjing University, Nanjing, Jiangsu, 210093, China, China |
2. | Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210093 |
References:
[1] |
S. Antonsev, A. Kazhikhov and V. Monakov, Boundary Value Problems in Mechanics of Nonhomogeneous Fluids,, Translated from the Russian, (1990).
|
[2] |
H. Beirao da Veiga, Diffusion on viscous fluids: Existence and asymptotic properties of solutions,, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 10 (1983), 341.
|
[3] |
D. Bresch, El. H. Essoufi and M. Sy, Effect of density dependent viscosities on multiphasic incompressible fluid models,, J. Math. Fluid Mech., 9 (2007), 377.
doi: 10.1007/s00021-005-0204-4. |
[4] |
X. Cai, L. Liao and Y. Sun, Global regularity for the initial value problem of a 2-D Kazhikhov-Smagulov type model,, Nonlinear Anal., 75 (2012), 5975.
doi: 10.1016/j.na.2012.06.011. |
[5] |
P. Constantin and C. Foias, Navier-Stokes Equations,, Chicago Lectures in Mathematics. University of Chicago Press, (1988).
|
[6] |
P. Embid, Well-posedness of the nonlinear equations for zero Mach number combustion,, Comm. PDE, 12 (1987), 1227.
doi: 10.1080/03605308708820526. |
[7] |
P. Embid, On the reactive and nondiffusive equations for zero Mach number flow,, Comm. PDE, 14 (1989), 1249.
doi: 10.1080/03605308908820652. |
[8] |
A. Kazhikhov and Sh. Smagulov, The correctness of boundary value problems in a diffusion model of an inhomogeneous fluid,, Sov. Phys. Dokl., 22 (1977), 249. Google Scholar |
[9] |
O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'tceva, Linear and Quasi-Linear Parabolic Equations,, Amer. Math. Soc., (1968). Google Scholar |
[10] |
P.-L. Lions, Mathematical Topics in Fluid Dynamics, Vol. 1, Incompressible Models,, Oxford Lecture Series in Mathematics and its Applications, (1996).
|
[11] |
A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Dimensions,, Appl. Math. Sci., (1984).
doi: 10.1007/978-1-4612-1116-7. |
[12] |
P. Secchi, On the initial value problem for the equations of motion of viscous incompressible fluids in the presence of diffusion,, Boll. Un. Mat. Ital., 1 (1982), 1117.
|
[13] |
P. Secchi, On the motion of viscous fluids in the presence of diffusion,, SIAM J. Math. Anal., 19 (1988), 22.
doi: 10.1137/0519002. |
[14] |
V. A. Solonnikov, $L^p$-estimates for solutions to the initial boundary-value problem for the generalized Stokes system in a bounded domain,, J. Math. Sci., 105 (2001), 2448.
doi: 10.1023/A:1011321430954. |
[15] |
Y. Sun and Z. Zhang, Global regularity for the initial-boundary value problem of the 2-D Boussinesq system with variable viscosity and thermal diffusivity,, J. Diff. Equa., 225 (2013), 1069.
doi: 10.1016/j.jde.2013.04.032. |
[16] |
C. Wang and Z. Zhang, Global well-posedness for the 2-D Boussinesq system with the temperature-dependent viscosity and thermal diffusivity,, Adv. in Math., 228 (2011), 43.
doi: 10.1016/j.aim.2011.05.008. |
show all references
References:
[1] |
S. Antonsev, A. Kazhikhov and V. Monakov, Boundary Value Problems in Mechanics of Nonhomogeneous Fluids,, Translated from the Russian, (1990).
|
[2] |
H. Beirao da Veiga, Diffusion on viscous fluids: Existence and asymptotic properties of solutions,, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 10 (1983), 341.
|
[3] |
D. Bresch, El. H. Essoufi and M. Sy, Effect of density dependent viscosities on multiphasic incompressible fluid models,, J. Math. Fluid Mech., 9 (2007), 377.
doi: 10.1007/s00021-005-0204-4. |
[4] |
X. Cai, L. Liao and Y. Sun, Global regularity for the initial value problem of a 2-D Kazhikhov-Smagulov type model,, Nonlinear Anal., 75 (2012), 5975.
doi: 10.1016/j.na.2012.06.011. |
[5] |
P. Constantin and C. Foias, Navier-Stokes Equations,, Chicago Lectures in Mathematics. University of Chicago Press, (1988).
|
[6] |
P. Embid, Well-posedness of the nonlinear equations for zero Mach number combustion,, Comm. PDE, 12 (1987), 1227.
doi: 10.1080/03605308708820526. |
[7] |
P. Embid, On the reactive and nondiffusive equations for zero Mach number flow,, Comm. PDE, 14 (1989), 1249.
doi: 10.1080/03605308908820652. |
[8] |
A. Kazhikhov and Sh. Smagulov, The correctness of boundary value problems in a diffusion model of an inhomogeneous fluid,, Sov. Phys. Dokl., 22 (1977), 249. Google Scholar |
[9] |
O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'tceva, Linear and Quasi-Linear Parabolic Equations,, Amer. Math. Soc., (1968). Google Scholar |
[10] |
P.-L. Lions, Mathematical Topics in Fluid Dynamics, Vol. 1, Incompressible Models,, Oxford Lecture Series in Mathematics and its Applications, (1996).
|
[11] |
A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Dimensions,, Appl. Math. Sci., (1984).
doi: 10.1007/978-1-4612-1116-7. |
[12] |
P. Secchi, On the initial value problem for the equations of motion of viscous incompressible fluids in the presence of diffusion,, Boll. Un. Mat. Ital., 1 (1982), 1117.
|
[13] |
P. Secchi, On the motion of viscous fluids in the presence of diffusion,, SIAM J. Math. Anal., 19 (1988), 22.
doi: 10.1137/0519002. |
[14] |
V. A. Solonnikov, $L^p$-estimates for solutions to the initial boundary-value problem for the generalized Stokes system in a bounded domain,, J. Math. Sci., 105 (2001), 2448.
doi: 10.1023/A:1011321430954. |
[15] |
Y. Sun and Z. Zhang, Global regularity for the initial-boundary value problem of the 2-D Boussinesq system with variable viscosity and thermal diffusivity,, J. Diff. Equa., 225 (2013), 1069.
doi: 10.1016/j.jde.2013.04.032. |
[16] |
C. Wang and Z. Zhang, Global well-posedness for the 2-D Boussinesq system with the temperature-dependent viscosity and thermal diffusivity,, Adv. in Math., 228 (2011), 43.
doi: 10.1016/j.aim.2011.05.008. |
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