Navier-Stokes: Singularities and Bifurcations
This article presents substantial advances in the analysis of the Navier-Stokes equations for both compressible and incompressible fluids, focusing on the formation of singularities, hypercomplex bifurcations, and regularity in Sobolev and Besov spaces. Through new theorems, we extend the theory of...
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| Format: | Article |
| Language: | English |
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Universidade Federal de Viçosa (UFV)
2024-10-01
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| Series: | The Journal of Engineering and Exact Sciences |
| Subjects: | |
| Online Access: | https://periodicos.ufv.br/jcec/article/view/19879 |
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| author | Rômulo Damasclin Chaves dos Santos Jorge Henrique de Oliveira Sales |
| author_facet | Rômulo Damasclin Chaves dos Santos Jorge Henrique de Oliveira Sales |
| author_sort | Rômulo Damasclin Chaves dos Santos |
| collection | DOAJ |
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This article presents substantial advances in the analysis of the Navier-Stokes equations for both compressible and incompressible fluids, focusing on the formation of singularities, hypercomplex bifurcations, and regularity in Sobolev and Besov spaces. Through new theorems, we extend the theory of singularities in fluid dynamics and introduce quaternionic bifurcations, representing an innovative extension of classical bifurcation theory. Moreover, we delve into the investigation of the regularity of compressible fluids, exploring the conditions under which solutions remain smooth or develop singularities. These contributions are fundamental to the understanding of global regularity issues, directly linked to the renowned Millennium Prize problem, which seeks definitive answers on the existence and smoothness of solutions to the Navier-Stokes equations. Additionally, we discuss how these theoretical advancements offer new approaches to unresolved problems related to the formation of singularities in turbulent flows and the multiscale behavior of solutions, which are crucial for a comprehensive understanding of fluid dynamics. This work not only broadens the scope of traditional mathematical analysis of the Navier-Stokes equations but also establishes a robust theoretical framework for the investigation of bifurcations and regularity in advanced functional spaces, fostering a deeper understanding of global regularity phenomena and the complex dynamics governing fluid systems.
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| format | Article |
| id | doaj-art-4c96ddba9c604fdca3a2f861b449237b |
| institution | Kabale University |
| issn | 2527-1075 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | Universidade Federal de Viçosa (UFV) |
| record_format | Article |
| series | The Journal of Engineering and Exact Sciences |
| spelling | doaj-art-4c96ddba9c604fdca3a2f861b449237b2025-02-02T19:53:21ZengUniversidade Federal de Viçosa (UFV)The Journal of Engineering and Exact Sciences2527-10752024-10-0110910.18540/jcecvl10iss9pp19879Navier-Stokes: Singularities and BifurcationsRômulo Damasclin Chaves dos Santos0Jorge Henrique de Oliveira Sales1Technological Institute of Aeronautics, BrazilSanta Cruz State University, Brazil This article presents substantial advances in the analysis of the Navier-Stokes equations for both compressible and incompressible fluids, focusing on the formation of singularities, hypercomplex bifurcations, and regularity in Sobolev and Besov spaces. Through new theorems, we extend the theory of singularities in fluid dynamics and introduce quaternionic bifurcations, representing an innovative extension of classical bifurcation theory. Moreover, we delve into the investigation of the regularity of compressible fluids, exploring the conditions under which solutions remain smooth or develop singularities. These contributions are fundamental to the understanding of global regularity issues, directly linked to the renowned Millennium Prize problem, which seeks definitive answers on the existence and smoothness of solutions to the Navier-Stokes equations. Additionally, we discuss how these theoretical advancements offer new approaches to unresolved problems related to the formation of singularities in turbulent flows and the multiscale behavior of solutions, which are crucial for a comprehensive understanding of fluid dynamics. This work not only broadens the scope of traditional mathematical analysis of the Navier-Stokes equations but also establishes a robust theoretical framework for the investigation of bifurcations and regularity in advanced functional spaces, fostering a deeper understanding of global regularity phenomena and the complex dynamics governing fluid systems. https://periodicos.ufv.br/jcec/article/view/19879Navier-Stokes.Singularities.Bifurcations.Regularity.Sobolev and Besov Spaces. |
| spellingShingle | Rômulo Damasclin Chaves dos Santos Jorge Henrique de Oliveira Sales Navier-Stokes: Singularities and Bifurcations The Journal of Engineering and Exact Sciences Navier-Stokes. Singularities. Bifurcations. Regularity. Sobolev and Besov Spaces. |
| title | Navier-Stokes: Singularities and Bifurcations |
| title_full | Navier-Stokes: Singularities and Bifurcations |
| title_fullStr | Navier-Stokes: Singularities and Bifurcations |
| title_full_unstemmed | Navier-Stokes: Singularities and Bifurcations |
| title_short | Navier-Stokes: Singularities and Bifurcations |
| title_sort | navier stokes singularities and bifurcations |
| topic | Navier-Stokes. Singularities. Bifurcations. Regularity. Sobolev and Besov Spaces. |
| url | https://periodicos.ufv.br/jcec/article/view/19879 |
| work_keys_str_mv | AT romulodamasclinchavesdossantos navierstokessingularitiesandbifurcations AT jorgehenriquedeoliveirasales navierstokessingularitiesandbifurcations |