On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles

Kunio Hidano, Jason Metcalfe, Hart F. Smith, Christopher D. Sogge, Yi Zhou
2009 Transactions of the American Mathematical Society  
We establish the Strauss conjecture concerning small-data global existence for nonlinear wave equations, in the setting of exterior domains to compact obstacles, for space dimensions n = 3 and 4. The obstacle is assumed to be nontrapping, and the solution is assumed to satisfy either Dirichlet or Neumann conditions along the boundary of the obstacle. The key step in the proof is establishing certain "abstract Strichartz estimates" for the linear wave equation on exterior domains. Reverts to
more » ... ins. Reverts to public domain 28 years from publication 2809 39. B. R. Vainberg: The short-wave asymptotic behavior of the solutions of stationary problems, and the asymptotic behavior as t → ∞ of the solutions of nonstationary problems, Russian Math. Surveys 30 (1975), 1-58. MR0415085 (54:3176) 40. Y. Zhou: Cauchy problem for semilinear wave equations with small data in four space dimensions, J. Partial Differential Equations 8 (1995), 135-144. MR1331521 (96c:35128)
doi:10.1090/s0002-9947-09-05053-3 fatcat:ylq7ynwrlnebnggu52qmvs43iy