Uniqueness of conservative solutions for the Hunter-Saxton equation
Abstract
We show that the Hunter-Saxton equation $u_t+uu_x=\frac14\big(\int_{-\infty}^x d\mu(t,z)- \int^{\infty}_x d\mu(t,z)\big)$ and $\mu_t+(u\mu)_x=0$ has a unique, global, weak, and conservative solution $(u,\mu)$ of the Cauchy problem on the line.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2021
- DOI:
- 10.48550/arXiv.2107.12681
- arXiv:
- arXiv:2107.12681
- Bibcode:
- 2021arXiv210712681G
- Keywords:
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- Mathematics - Analysis of PDEs;
- 35A02;
- 35L45;
- 35B60
- E-Print:
- 54 pages