Details

Autor(en) / Beteiligte

• Lai, Ning-An
• Schiavone, Nico Michele

Titel

Blow-up and lifespan estimate for generalized Tricomi equations related to Glassey conjecture

Ist Teil von

• Mathematische Zeitschrift, 2022-08, Vol.301 (4), p.3369-3393

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2022

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We study in this paper the small data Cauchy problem for the semilinear generalized Tricomi equations with a nonlinear term of derivative type u tt - t 2 m Δ u = | u t | p for m ≥ 0 . Blow-up result and lifespan estimate from above are established for 1 < p ≤ 1 + 2 ( m + 1 ) ( n - 1 ) - m . If m = 0 , our results coincide with those of the semilinear wave equation. The novelty consists in the construction of a new test function, by combining cut-off functions, the modified Bessel function of second kind and a (generalized) eigenfunction of the Laplacian. Interestingly, if n = 2 the blow-up power is independent of m . We also furnish a local existence result, which implies the optimality of lifespan estimate at least in the 1-dimensional case.