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Concerning Ill-posedness for Semilinear Wave Equations by Liu, Mengyun; Wang, Chengbo is a scholarly article available to read on EtoBox.

What is Concerning Ill-posedness for Semilinear Wave Equations about?

In this paper, we investigate the problem of optimal regularity for derivative semilinear wave equations to be locally well-posed in $H^{s}$ with spatial dimension $n \leq 5$. We show this equation, with power $2\le p\le 1+4/(n-1)$, is (strongly) ill-posed in $H^{s}$ with $s = (n+5)/4$ in general. Moreover, when the nonlinearity is quadratic we establish a characterization of the structure of nonlinear terms in terms of the regularity. As a byproduct, we give an alternative proof of the failure of the local in time endpoint scale-invariant $L_{t}^{4/(n-1)}L_{x}^{\infty}$ Strichartz estimates. Finally, as an application, we also prove ill-posed results for some semilinear half wave equations.

Author

Liu, Mengyun; Wang, Chengbo

Published

2018

Language

EN