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Nonexistence of positive solutions for a system of integral equations on $R^n_+$ and applications
A stability result for the Stokes-Boussinesq equations in infinite 3d channels
1. | University of Pittsburgh, Department of Mathematics, 301 Thackeray Hall, Pittsburgh, PA 15260, United States |
2. | Isfahan University of Technology, Isfahan, Iran |
References:
[1] |
S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II,, Comm. Pure Appl. Math., 17 (1964), 35.
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[2] |
Henri Berestycki, "Some Nonlinear PDE's in the Theory of Flame Propagation,", ICIAM 99 (Edinburgh), (1322).
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[3] |
Henri Berestycki, Peter Constantin and Lenya Ryzhik, Non-planar fronts in Boussinesq reactive flows,, Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire, 23 (2006), 407.
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[4] |
Peter Constantin, Alexander Kiselev and Lenya Ryzhik, Fronts in reactive convection: bounds, stability, and instability,, Comm. Pure Appl. Math., 56 (2003), 1781.
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[5] |
Peter Constantin, Alexander Kiselev, Lenya Ryzhik and Andrej Zlatoš, Diffusion and mixing in fluid flow,, Ann. of Math., 168 (2008), 643.
|
[6] |
Peter Constantin, Marta Lewicka and Lenya Ryzhik, Travelling waves in two-dimensional reactive Boussinesq systems with no-slip boundary conditions,, Nonlinearity, 19 (2006), 2605.
|
[7] |
Peter Constantin, Alexei Novikov and Lenya Ryzhik, Relaxation in reactive flows,, Geom. Funct. Anal., 18 (2008), 1145.
|
[8] |
Marta Lewicka, Existence of traveling waves in the Stokes-Boussinesq system for reactive flows,, J. Differential Equations, 237 (2007), 343.
|
[9] |
Jian-Guo Liu, Jie Liu and Robert L. Pego, Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate,, Comm. Pure Appl. Math., 60 (2007), 1443.
|
[10] |
Marta Lewicka and Piotr B. Mucha, On the existence of traveling waves in the 3D Boussinesq system,, Comm. Math. Phys., 292 (2009), 417.
|
[11] |
Rozenn Texier-Picard and Vitaly Volpert, Problèmes de réaction-diffusion-convection dans des cylindres non bornés,, C. R. Acad. Sci. Paris S\'er. I Math., 333 (2001), 1077.
|
[12] |
Wenzheng Xie, A sharp pointwise bound for functions with $L^2$-Laplacians on arbitrary domains and its applications,, Bull. Amer. Math. Soc. (N.S.), 26 (1992), 294.
|
[13] |
Ya. B. Zeldovich, G. I. Barenblatt, V. B. Librovich and G. M. Makhviladze, "The Mathematical Theory of Combustion and Explosions,", Consultants Bureau [Plenum], (1985).
|
show all references
References:
[1] |
S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II,, Comm. Pure Appl. Math., 17 (1964), 35.
|
[2] |
Henri Berestycki, "Some Nonlinear PDE's in the Theory of Flame Propagation,", ICIAM 99 (Edinburgh), (1322).
|
[3] |
Henri Berestycki, Peter Constantin and Lenya Ryzhik, Non-planar fronts in Boussinesq reactive flows,, Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire, 23 (2006), 407.
|
[4] |
Peter Constantin, Alexander Kiselev and Lenya Ryzhik, Fronts in reactive convection: bounds, stability, and instability,, Comm. Pure Appl. Math., 56 (2003), 1781.
|
[5] |
Peter Constantin, Alexander Kiselev, Lenya Ryzhik and Andrej Zlatoš, Diffusion and mixing in fluid flow,, Ann. of Math., 168 (2008), 643.
|
[6] |
Peter Constantin, Marta Lewicka and Lenya Ryzhik, Travelling waves in two-dimensional reactive Boussinesq systems with no-slip boundary conditions,, Nonlinearity, 19 (2006), 2605.
|
[7] |
Peter Constantin, Alexei Novikov and Lenya Ryzhik, Relaxation in reactive flows,, Geom. Funct. Anal., 18 (2008), 1145.
|
[8] |
Marta Lewicka, Existence of traveling waves in the Stokes-Boussinesq system for reactive flows,, J. Differential Equations, 237 (2007), 343.
|
[9] |
Jian-Guo Liu, Jie Liu and Robert L. Pego, Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate,, Comm. Pure Appl. Math., 60 (2007), 1443.
|
[10] |
Marta Lewicka and Piotr B. Mucha, On the existence of traveling waves in the 3D Boussinesq system,, Comm. Math. Phys., 292 (2009), 417.
|
[11] |
Rozenn Texier-Picard and Vitaly Volpert, Problèmes de réaction-diffusion-convection dans des cylindres non bornés,, C. R. Acad. Sci. Paris S\'er. I Math., 333 (2001), 1077.
|
[12] |
Wenzheng Xie, A sharp pointwise bound for functions with $L^2$-Laplacians on arbitrary domains and its applications,, Bull. Amer. Math. Soc. (N.S.), 26 (1992), 294.
|
[13] |
Ya. B. Zeldovich, G. I. Barenblatt, V. B. Librovich and G. M. Makhviladze, "The Mathematical Theory of Combustion and Explosions,", Consultants Bureau [Plenum], (1985).
|
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