Strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation

By D. Tataru. 2000

206 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f2694ee7a0c7c75c9d5b72fb59a14fd50b371974

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Citations in the corpus

Life-Span of Solutions to Critical Semilinear Wave Equations (2011, methodology): “Later, a simple proof was given by Tataru [19] in the case p > p0 n and n ≥ 4.”
Concerning the wave equation on asymptotically Euclidean manifolds (2008, background): “uation, Amer. J. Math., 122(2000), no.2, 349–376. [35] D. Tataru, Strichartz estimates for second order hyperbolic operators with nonsmooth coeﬃ- cients. II, Amer. J. Math., 123(2001), no.3, 385–423. [36] D. Tataru, Strichartz estimates in the hyperbolic space and global existence for the semilinear”
Weighted Strichartz estimates with angular regularity and their applications (2008, background): “This conjecture was finally completed by Georgiev-Lindblad-Sogge in [9] (see also Tataru [36] for another proof).”
Some constructions for the fractional Laplacian on noncompact manifolds (2012, unknown): “For stratified Lie groups or symmetric spaces (see [27] and [2]; see also §3 of [63] for hyperbolic space), the following equivalence was proved: H p (M) = { f ∈ L(M), ‖f‖Lp(M) + ‖(−Δ)γ/2 f‖Lp(M) <∞ } .”
Semilinear Schrödinger flows on hyperbolic spaces: scattering in H1 (2008, background): “These two definitions agree (see, for example, [ 44, Section 3 ]).”
The wave equation on hyperbolic spaces (2010, background): “Notice that Tataru [30] obtained dispersive estimates with exponential decay in time for the operators cos tD and sin tD D , but did not prove actual Strichartz estimates.”
Nonexistence of global solutions for the semilinear Moore – Gibson – Thompson equation in the conservative case (2019, background): “According to [17, 21, 39, 12, 13, 38, 37, 49, 27, 11, 42, 16, 45, 50, 22] the so – called Strauss exponent pStr(n) is the critical exponent of (1.”
Semi‐linear wave models with power non‐linearity and scale‐invariant time‐dependent mass and dissipation (2017, background): “For p0(n) < p ≤ n+3 n−1 , n > 1, the global existence (in time) of small data energy solutions was proved, see, for example, [9], [10], [14], [22], [29].”
Critical Exponent for a Nonlinear Wave Equation with Damping (2000, background): “La preuve de cette circonstance, connue sous le nom de conjecture de Strauss, a requis presque vingt ans d’efforts de nombreux mathématiciens, à commencer par Glassey [3], John [4], Sideris [7], Zhou [10], pour finir avec Lindblad et Sogge [6], Georgiev, Lindblad et Sogge [2], et Tataru [9].”
A shift in the Strauss exponent for semilinear wave equations with a not effective damping (2015, background): “ite time for a suitable choice of initial data (see [9], [13], [14], [20], [21], [24]), whereas for p∈ (p0(n),(n+ 3)/(n− 1)] a unique global (in time) small data solution exists (see [8], [10], [13], [22], [28]). In space dimension n= 1, solutions to (2) blow-up in ﬁnite time for any p>1, hence, ”
On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles (2008, background): “A key step in the proof of Theorem 1.4 will be to establish the following result that is implicit in [4].”
Finite time blow up for critical wave equations in high dimensions (2004, background): “Step 4. For any function f ∈ L p (R), we introduce the transformation (2.16) T (f)(�) =”