On the existence of global strong solutions to 1D bilayer shallow water model
Brahima, R., Julien, Z., Mohamed Bassirou, B., Yacouba, Z., Jean de Dieu, Z. (2024). On the existence of global strong solutions to 1D bilayer shallow water model. EKB Journal Management System, 12(1), 1-12. doi: 10.21608/ejmaa.2023.193654.1006
ROAMBA Brahima; ZONGO Julien; BAMOGO Mohamed Bassirou; ZONGO Yacouba; ZABSONRE Jean de Dieu. "On the existence of global strong solutions to 1D bilayer shallow water model". EKB Journal Management System, 12, 1, 2024, 1-12. doi: 10.21608/ejmaa.2023.193654.1006
Brahima, R., Julien, Z., Mohamed Bassirou, B., Yacouba, Z., Jean de Dieu, Z. (2024). 'On the existence of global strong solutions to 1D bilayer shallow water model', EKB Journal Management System, 12(1), pp. 1-12. doi: 10.21608/ejmaa.2023.193654.1006
Brahima, R., Julien, Z., Mohamed Bassirou, B., Yacouba, Z., Jean de Dieu, Z. On the existence of global strong solutions to 1D bilayer shallow water model. EKB Journal Management System, 2024; 12(1): 1-12. doi: 10.21608/ejmaa.2023.193654.1006

On the existence of global strong solutions to 1D bilayer shallow water model

Electronic Journal of Mathematical Analysis and Applications
Volume 12, Issue 1, January 2024, Page 1-12  XML PDF (523.55 K)
Document Type: Regular research papers
DOI: 10.21608/ejmaa.2023.193654.1006
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Authors
ROAMBA Brahima email 1; ZONGO Julien2; BAMOGO Mohamed Bassirou3; ZONGO Yacouba4; ZABSONRE Jean de Dieu5
1Institut Universitaire de Technologie, Université Nazi Boni, Bobo-Dioulasso, Burkina Faso.
2UFR/SEA, Université Nazi Boni, Bobo-Dioulasso, Burhina Faso.
3UFR/SEA, Université Nazi Boni, Bobo-Dioulasso, Burkina Faso.
4EPO, Université Ouaga 2S, Ouagadougou, Burkina Faso
5UFR/SEA, Université Nazi boni, Bobo-Dioulasso, Burkina Faso
Abstract
Our study focuses on 1D viscous bilayers shallow water model. The model considered is represented by two superposed immiscible fluids with different physical properties. Each layer is governed by the shallow water equations in one dimension. A regularized model of the considered model has been the subject of some recent studies. Endeed, to do this, the authors considered an approximate model ( by introducing a parameter epsilon ) for which they prove the existence of global strong solutions. But note that when repsilon tends towards 0, they obtain the existence of strong solution of the stationary model. Our contribution is to extend the results of the work carried out in [Nonlinear Analysis, vol (14)2, 1216-1124, (2013)] by proving the existence of global strong solutions of the considered model. The key point of this proof is based on an estimate of a new entropy called '' mathematical BD entropy" which gives additional regularities. Also, we follow the approach used ba the autheurs in [Math Nachr. 291 (14-15), 2183-2203, (2018)] to be able the limit water heigh.
Keywords
shallow water equations; bilayer model; viscous
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