Existence of global weak solutions to 2D reduced gravity two-and-a-half layer model |
| |
Institution: | 1. School of Mathematical Sciences, Beihang University, 100191 Beijing, China;2. Academy of Mathematics & Systems Science and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, China;3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;1. School of Mathematical Sciences, LSC-MOE and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China;2. Department of Mathematics, City University of Hong Kong, Hong Kong, China |
| |
Abstract: | We study the global existence of weak solutions to a reduced gravity two-and-a-half layer model appearing in oceanic fluid dynamics in two-dimensional torus. Based on Faedo–Galerkin method and weak convergence method, we construct the global weak solutions which are renormalized in velocity variable, where the technique of renormalized solutions was introduced by Lacroix-Violet and Vasseur (2018). Besides, we prove that the renormalized solutions are weak solutions, which satisfy the basic energy inequality and Bresch–Desjardins entropy inequality, but not the Mellet–Vasseur type inequality. In the proof, we use the reduced gravity two-and-a-half layer model with drag forces and capillary term as approximate system. It should be pointed out that only when the capillary term vanishes, we prove the existence of renormalized solution to the approximation system, which is different from Lacroix-Violet and Vasseur (2018) with the quantum potential. |
| |
Keywords: | Two-and-a-half layer model Global weak solutions Bresch–Desjardins entropy |
本文献已被 ScienceDirect 等数据库收录! |
|