Heat-flow monotonicity of Strichartz norms

By Jonathan Bennett, Neal Bez, Anthony Carbery, Dirk Hundertmark. 2008

77 citations recorded by the source corpus.

Most notably we prove that for $d=1,2$ the classical Strichartz norm $$\|e^{i s\Delta}f\|_{L^{2+4/d}_{s,x}(\mathbb{R}\times\mathbb{R}^d)}$$ associated to the free Schr\"{o}dinger equation is nondecreasing as the initial datum $f$ evolves under a certain quadratic heat-flow.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/360709961883cd54f2be599c3c070560de5149c8

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

The geodesic X-ray transform with fold caustics (2010, methodology): “Another proof that Gaussians extremize the inequality is in [Bennett et al. 2009].”
Maximizers for the Stein–Tomas Inequality (2016, unknown): “In fact, by a remarkable work of Foschi [14] (see also [21, 5]), the value of SN−1 is known for N = 2 and N = 3.”
The linear profile decomposition for the Airy equation and the existence of maximizers for the Airy Strichartz inequality (2008, unknown): “Hence these sequences”
Maximizers for the Strichartz and the Sobolev-Strichartz inequalities for the Schrödinger equation (2009, unknown): “... inequality and the space-time Fourier transform; Hundertmark and Zharnitsky [9] independently obtained this result by an interesting representation formula of the Strichartz inequalities; recently, Carneiro [6] proved a sharp Strichartz-type inequality by following the arguments in [9] and found”
Existence of Extremals for a Fourier Restriction Inequality (2010, methodology): “Another proof that Gaussians extremize the inequality is in [Bennett et al. 2009].”