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PDE Real Analysis Seminar
Seminar information archive ～05/23｜Next seminar｜Future seminars 05/24～
| Date, time & place | Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Yoshikazu Giga, Kazuhiro Ishige, Hiroyoshi Mitake, Tsuyoshi Yoneda |
| URL | https://www.math.sci.hokudai.ac.jp/coe/sympo/pde_ra/index_en.html |
2016/07/12
14:20-15:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Amru Hussein (TU Darmstadt)
Global Strong $L^p$ Well-Posedness of the 3D Primitive Equations (English)
Amru Hussein (TU Darmstadt)
Global Strong $L^p$ Well-Posedness of the 3D Primitive Equations (English)
[ Abstract ]
Primitive Equations are considered to be a fundamental model for geophysical flows. Here, the $L^p$ theory for the full primitive equations, i.e. the three dimensional primitive equations coupled to the equation for temperature and salinity, is developed. This set of equations is globally strongly well-posed for arbitrary large initial data lying in certain interpolation spaces, which are explicitly characterized as subspaces of $H^2/p$, $p$, $1 < p < \infty$, satisfying certain boundary conditions. Thus, the general $L^p$ setting admits rougher data than the usual $L^2$ theory with initial data in $H^1$.
In this study, the linearized Stokes type problem plays a prominent role, and it turns out that it can be treated efficiently using perturbation methods for $H^\infty$-calculus.
Primitive Equations are considered to be a fundamental model for geophysical flows. Here, the $L^p$ theory for the full primitive equations, i.e. the three dimensional primitive equations coupled to the equation for temperature and salinity, is developed. This set of equations is globally strongly well-posed for arbitrary large initial data lying in certain interpolation spaces, which are explicitly characterized as subspaces of $H^2/p$, $p$, $1 < p < \infty$, satisfying certain boundary conditions. Thus, the general $L^p$ setting admits rougher data than the usual $L^2$ theory with initial data in $H^1$.
In this study, the linearized Stokes type problem plays a prominent role, and it turns out that it can be treated efficiently using perturbation methods for $H^\infty$-calculus.
