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Bilinear space-time estimates for homogeneous wave equations. (English) Zbl 0959.35107
The authors investigate space-time regularity properties of the products and bilinear forms of solutions of the homogeneous wave equation in terms of the regularity of the initial data. The main result of the paper gives necessary and sufficient conditions (involving the exponents of derivatives) for the validity of \(L^2\) estimates. For more general estimates in \(L^q_t L^r_x\) spaces, the authors give necessary conditions and formulate some conjectures.
Reviewer: C.Popa (Iaşi)

MSC:
35L05 Wave equation
35B45 A priori estimates in context of PDEs
35B65 Smoothness and regularity of solutions to PDEs
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