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PDE Real Analysis Seminar
Seminar information archive ～06/23｜Next seminar｜Future seminars 06/24～
| 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 Lp Well-Posedness of the 3D Primitive Equations (English)
Amru Hussein (TU Darmstadt)
Global Strong Lp Well-Posedness of the 3D Primitive Equations (English)
[ Abstract ]
Primitive Equations are considered to be a fundamental model for geophysical flows. Here, the Lp 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 H2/p, p, 1<p<∞, satisfying certain boundary conditions. Thus, the general Lp setting admits rougher data than the usual L2 theory with initial data in H1.
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∞-calculus.
Primitive Equations are considered to be a fundamental model for geophysical flows. Here, the Lp 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 H2/p, p, 1<p<∞, satisfying certain boundary conditions. Thus, the general Lp setting admits rougher data than the usual L2 theory with initial data in H1.
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∞-calculus.
