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- W4288804553 abstract "In this paper, we use the method of convex integration to construct infinitely many distributional solutions in $H^{beta}$ for $0<betall1$ 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 $0$." @default.
- W4288804553 created "2022-07-30" @default.
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- W4288804553 date "2022-07-28" @default.
- W4288804553 modified "2023-09-27" @default.
- W4288804553 title "Construction of solutions to the 3D Euler equations with initial data in $H^beta$ for $beta>0$" @default.
- W4288804553 doi "https://doi.org/10.48550/arxiv.2207.14041" @default.
- W4288804553 hasPublicationYear "2022" @default.
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