Construction of solutions to the 3D Euler equations with initial data in $H^\beta$ for $\beta>0$
| Autor: | Khor, Calvin, Miao, Changxing |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we use the method of convex integration to construct infinitely many distributional solutions in $H^{\beta}$ for $0<\beta\ll1$ to the initial value problem for the three-dimensional incompressible Euler equations. We show that if the initial data has any small fractional derivative in $L^2$, then we can construct solutions with some regularity, so that the corresponding $L^2$ energy is continuous in time. This is distinct from the $L^2$ existence result of E. Wiedemann, Ann. Inst. Henri Poincar\'e, Anal. Non Lin\'eaire 28, No. 5, 727--730 (2011; Zbl 1228.35172), where the energy is discontinuous at $0$. Comment: 35 pages, 1 figure |
| Databáze: | arXiv |
| Externí odkaz: |
|