Global solvability for nonlinear wave equations with singular potential. (English) Zbl 1523.35222
Summary: In this work we consider the so-called Strauss conjecture for 3D nonlinear wave equation with singular potential and provide a positive answer concerning the global existence part. The key point is to exploit the additional decay of the solution away from the light cone. For this purpose we derive appropriate conformal type energy estimates under repulsively condition on the potential. However, it is not obvious whether functions in a domain of the Friedrichs extension of the minus Laplacian with singular potential have \(H^2\)-regularity or not. To clarify this issue, we make use of the essential self-adjointness of the Schrödinger operator to obtain the desired property.
MSC:
| 35L71 | Second-order semilinear hyperbolic equations |
| 35B33 | Critical exponents in context of PDEs |
| 35L15 | Initial value problems for second-order hyperbolic equations |
| 35L81 | Singular hyperbolic equations |
Keywords:
nonlinear wave equation; singular potential; essentially self-adjointness; Strauss conjectureReferences:
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