Abstract: | We consider the Cauchy problem for second‐order strictly hyperbolic equations with time‐depending non‐regular coefficients. There is a possibility that singular coefficients make a regularity loss for the solution. The main purpose of this paper is to derive an optimal singularity for the coefficient that the Cauchy problem is C∞ well‐posed. Moreover, we will apply such a result to the estimate of the existence time of the solution for Kirchhoff equation. Copyright © 2003 John Wiley & Sons, Ltd. |