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arXiv · 2009.03967

Infinite norm of the derivative of the solution operator of Euler equations

Y. Charles Li
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Abstract

Through a simple and elegant argument, we prove that the norm of the derivative of the solution operator of Euler equations posed in the Sobolev space $H^n$, along any base solution that is in $H^n$ but not in $H^{n+1}$, is infinite. We also review the counterpart of this result for Navier-Stokes equations at high Reynolds number from the perspective of fully developed turbulence. Finally we present a few examples and numerical simulations to show a more complete picture of the so-called rough dependence upon initial data.

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Y. Charles Li. 2020-09-08. Infinite norm of the derivative of the solution operator of Euler equations. https://doi.org/10.1063/5.0043862

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