The Derivative Structure for a Quadratic Nonlinearity and Uniqueness for SQG
| Autor: | Iwabuchi, Tsukasa |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study the two-dimensional surface quasi-geostrophic equation on a bounded domain with a smooth boundary. Motivated by the three-dimensional incompressible Navier-Stokes equations and previous results in the entire space $\mathbb R^2$, we demonstrate that the uniqueness of the mild solution holds in $L^2$. For the proof, we provide a method for handling fractional Laplacians in nonlinear problems, and develop an approach to derive second-order derivativesfor the nonlinear term involving fractional derivatives of the Dirichlet Laplacian. Comment: 20pages |
| Databáze: | arXiv |
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