On Right Continuity in $(L^2)^3$ at All the Points of Energy-regularized Solutions for the 3D Navier-Stokes Equations
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910523361067008 |
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| author | Kasyanov, Pavlo O. |
| author_facet | Kasyanov, Pavlo O. |
| contents | In this note I provide the notion of energy-regularized solutions (ER-solutions) of the 3D Navier-Stokes equations. These solutions can be obtained via the standard Galerkin arguments. I prove that each ER-solution for the 3D Navier-Stokes system satisfies Leray-Hopf property. Moreover, each ER-solution is rightly continuous in the standard phase space $H$ endowed with the strong convergence topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_05754 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Right Continuity in $(L^2)^3$ at All the Points of Energy-regularized Solutions for the 3D Navier-Stokes Equations Kasyanov, Pavlo O. Analysis of PDEs In this note I provide the notion of energy-regularized solutions (ER-solutions) of the 3D Navier-Stokes equations. These solutions can be obtained via the standard Galerkin arguments. I prove that each ER-solution for the 3D Navier-Stokes system satisfies Leray-Hopf property. Moreover, each ER-solution is rightly continuous in the standard phase space $H$ endowed with the strong convergence topology. |
| title | On Right Continuity in $(L^2)^3$ at All the Points of Energy-regularized Solutions for the 3D Navier-Stokes Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2301.05754 |