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Hokkaido University Preprint Series in Mathematics >
RIGOROUS JUSTIFICATION OF THE HYDROSTATIC APPROXIMATION FOR THE PRIMITIVE EQUATIONS BY SCALED NAVIER-STOKES EQUATIONS
| Title: | RIGOROUS JUSTIFICATION OF THE HYDROSTATIC APPROXIMATION FOR THE PRIMITIVE EQUATIONS BY SCALED NAVIER-STOKES EQUATIONS |
| Authors: | FURUKAWA, KEN Browse this author | | GIGA, YOSHIKAZU Browse this author | | HIEBER, MATTHIAS Browse this author | | HUSSEIN, AMRU Browse this author | | KASHIWABARA, TAKAHITO Browse this author | | WRONA, MARC Browse this author |
| Issue Date: | 10-Aug-2018 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1112 |
| Start Page: | 1 |
| End Page: | 10 |
| Abstract: | Consider the anisotropic Navier-Stokes equations as well as the primitive equations. It is shown that the horizontal velocity of the solution to the anisotropic Navier-Stokes equations in a cylindrical domain of height ε with initial data u0 = (v0,w0) ∈ B2−2/p q,p , 1/q + 1/p ≤ 1 if q ≥ 2 and 4/3q+2/3p ≤ 1 if q ≤ 2, converges as ε → 0 with convergence rateO(ε) to the horizontal velocity of the solution to the primitive equations with initial data v0 with respect to the maximal-Lp-Lq-regularity norm. Since the difference of the corresponding vertical velocities remains bounded with respect to that norm, the convergence result yields a rigorous justification of the hydrostatic approximation in the primitive equations in this setting. It generalizes in particular a result by Li and Titi for the L2-L2-setting. The approach presented here does not rely on second order energy estimates but on maximal Lp-Lq-estimates for the heat equation. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/71287 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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