INHOMOGENEOUS STRICHARTZ ESTIMATES

By Damiano Foschi. 2003

222 citations recorded by the source corpus.

We look for the optimal range of Lebesque exponents for which inhomogeneous Strichartz estimates are valid. It is known that this range is larger than the one given by admissible exponents for homogeneous estimates. We prove inhomogeneous estimates in this larger range adopting the abstract setting and interpolation techniques already used by Keel and Tao for the endpoint case of the homogeneous estimates. Applications to Schrodinger equations are given, which extend previous work by Kato.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/864f4508f2a6e3e88b28389cc0c5f203c689a344

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In Applied Mathematics

1. Rowan Killip
2. Carlos E. Kenig
3. Benoit Pausader
4. Xiaoyi Zhang
5. F. Merle
6. Monica Visan
7. B. Dodson
8. Aynur Bulut

In Mathematical Physics

1. Carlos E. Kenig
2. Rowan Killip
3. Monica Visan
4. B. Dodson
5. F. Merle
6. Xiaoyi Zhang
7. Aynur Bulut
8. Qing Guo

Citations in the corpus

• Scattering for the focusing L2-supercritical and Ḣ2-subcritical biharmonic NLS equations (2015, background): “Combining the results obtained by [22] and [28], we can infer the following inhomogeneous Strichartz estimates on I = [0,T]: ∥∥∥∥ ∫ t”
• Quintic NLS in the exterior of a strictly convex obstacle (2012, background): “The endpoint cases and exotic retarded estimates are more delicate; see [23, 40, 69].”
• Global well-posedness and scattering for nonlinear Schr\"odinger equations with combined nonlinearities in the radial case (2014, background): “tained in [22, 23]. We expect our result will be extended to higher dimensions(d ≥ 5) since all the arguments make sense except the long-time perturbation. However, the exotic Strichartz estimates in [11, 29] seem useless to establish the long-time perturbation in our case because the mass-critical ”
• Global Well-Posedness for Energy Critical Fourth-Order Schrodinger Equations in the Radial Case (2007, background): “(6.6) These spaces are involved in the following Exotic Strichartz estimates (6.7) which we obtain as a consequence of the result in Foschi [7].”
• Nonlinear Schrodinger Equations at Critical Regularity (2013, background): “For the largest set of exponents currently known (and a discussion of counterexamples), see [25, 101].”
• A Sharp Condition for Scattering of the Radial 3D Cubic Nonlinear Schrödinger Equation (2007, background): “We shall also need the Kato inhomogeneous Strichartz estimate [13] (for further extensions see [8] and [30])”
• Continuous dependence for NLS in fractional order spaces (2010, background): “4 For more general estimates of this type, see [14,10,25].”
• Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications (2008, result): “This estimate follows by results of Harmse [12], Oberlin [28], Foschi [8], Vilela [39] and Taggart [34].”