Steady Boussinesq system with mixed boundary conditions including friction conditions
Applications of Mathematics (2022)
- Volume: 67, Issue: 5, page 593-613
- ISSN: 0862-7940
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topKim, Tujin. "Steady Boussinesq system with mixed boundary conditions including friction conditions." Applications of Mathematics 67.5 (2022): 593-613. <http://eudml.org/doc/298490>.
@article{Kim2022,
abstract = {In this paper we are concerned with the steady Boussinesq system with mixed boundary conditions. The boundary conditions for fluid may include Tresca slip, leak, one-sided leak, velocity, vorticity, pressure and stress conditions together and the conditions for temperature may include Dirichlet, Neumann and Robin conditions together. For the problem involving the static pressure and stress boundary conditions, it is proved that if the data of the problem are small enough, then there exists a solution and the solution with small norm is unique. For the problem involving the total pressure and total stress boundary conditions, the existence of a solution is proved without smallness of the data.},
author = {Kim, Tujin},
journal = {Applications of Mathematics},
keywords = {heat-convection; variational inequality; mixed boundary conditions; Tresca slip; leak boundary conditions; one-sided leak; pressure boundary condition; existence and uniqueness},
language = {eng},
number = {5},
pages = {593-613},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Steady Boussinesq system with mixed boundary conditions including friction conditions},
url = {http://eudml.org/doc/298490},
volume = {67},
year = {2022},
}
TY - JOUR
AU - Kim, Tujin
TI - Steady Boussinesq system with mixed boundary conditions including friction conditions
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 5
SP - 593
EP - 613
AB - In this paper we are concerned with the steady Boussinesq system with mixed boundary conditions. The boundary conditions for fluid may include Tresca slip, leak, one-sided leak, velocity, vorticity, pressure and stress conditions together and the conditions for temperature may include Dirichlet, Neumann and Robin conditions together. For the problem involving the static pressure and stress boundary conditions, it is proved that if the data of the problem are small enough, then there exists a solution and the solution with small norm is unique. For the problem involving the total pressure and total stress boundary conditions, the existence of a solution is proved without smallness of the data.
LA - eng
KW - heat-convection; variational inequality; mixed boundary conditions; Tresca slip; leak boundary conditions; one-sided leak; pressure boundary condition; existence and uniqueness
UR - http://eudml.org/doc/298490
ER -
References
top- Acevedo, P., Amrouche, C., Conca, C., 10.1016/j.aml.2015.09.015, Appl. Math. Lett. 53 (2016), 39-44 9999DOI99999 10.1016/j.aml.2015.09.015 . (2016) Zbl1333.35175MR3426553DOI10.1016/j.aml.2015.09.015
- Alekseev, G. V., Smishliaev, A. B., Solvability of the boundary-value problems for Boussinesq equations with inhomogeneous boundary conditions, J. Math. Fluid Mech. 3 (2001), 18-39 9999DOI99999 10.1007/PL00000962 . (2001) Zbl0989.35106MR1830653
- Barbu, V., 10.1007/978-1-4419-5542-5, Springer Monographs in Mathematics. Springer, Berlin (2010). (2010) Zbl1197.35002MR2582280DOI10.1007/978-1-4419-5542-5
- Chebotarev, A. Y., 10.1023/A:1010267111548, Math. Notes 70 (2001), 264-274. (2001) Zbl1140.35548MR1882418DOI10.1023/A:1010267111548
- Gajewski, H., Gröger, K., Zacharias, K., Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Mathematische Lehrbücher und Monographien. II. Abteilung 38. Academie, Berlin (1974), German. (1974) Zbl0289.47029MR0636412
- Kim, H., The existence and uniqueness of very weak solutions of the stationary Boussinesq system, Nonlinear Anal., Theory Methods Appl., Ser. A 75 (2012), 317-330 9999DOI99999 10.1016/j.na.2011.08.035 . (2012) Zbl1229.35209MR2846803
- Kim, T., Cao, D., 10.1016/j.na.2014.09.017, Nonlinear Anal., Theory Methods Appl., Ser. A 113 (2015), 94-114. (2015) Zbl1304.35551MR3281848DOI10.1016/j.na.2014.09.017
- Kim, T., Cao, D., 10.4310/MAA.2016.v23.n4.a3, Methods Appl. Anal. 23 (2016), 329-364. (2016) Zbl1372.35116MR3633953DOI10.4310/MAA.2016.v23.n4.a3
- Kim, T., Cao, D., 10.4310/MAA.2020.v27.n2.a1, Methods Appl. Anal. 27 (2020), 87-124. (2020) Zbl1448.35241MR4143709DOI10.4310/MAA.2020.v27.n2.a1
- Kovtunov, D. A., 10.1134/S0012266109010091, Differ. Equ. 45 (2009), 73-85. (2009) Zbl1176.35137MR2597096DOI10.1134/S0012266109010091
- Morimoto, H., On the existence of weak solutions of equations of natural convection, J. Fac. Sci., Univ. Tokyo, Sect. I A 36 (1989), 87-102 9999MR99999 991021 . (1989) Zbl0676.76079MR0991021
- Morimoto, H., 10.3836/tjm/1270130501, Tokyo J. Math. 14 (1991), 217-226. (1991) Zbl0739.35074MR1108168DOI10.3836/tjm/1270130501
- Morimoto, H., 10.1619/fesi.53.213, Funkc. Ekvacioj, Ser. Int. 53 (2010), 213-229. (2010) Zbl1205.35315MR2730621DOI10.1619/fesi.53.213
- Naumann, J., Pokorný, M., Wolf, J., 10.1016/j.nonrwa.2011.11.018, Nonlinear Anal., Real World Appl. 13 (2012), 1600-1620. (2012) Zbl1254.76048MR2890996DOI10.1016/j.nonrwa.2011.11.018
- Villamizar-Roa, E. J., Rodríguez-Bellido, M. A., Rojas-Medar, M. A., 10.1016/j.crma.2006.06.011, C. R., Math., Acad. Sci. Paris 343 (2006), 191-196. (2006) Zbl1102.35031MR2246338DOI10.1016/j.crma.2006.06.011
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