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Two-and multi-phase quadrature surfaces
Sharp Strichartz estimates in spherical coordinates
Fakultät für Mathematik, Universität Bielefeld, Postfach 10 01 31,33501 Bielefeld, Germany |
We prove Strichartz estimates found after adding regularity in the spherical coordinates for Schrödinger-like equations. The obtained estimates are sharp up to endpoints. The proof relies on estimates involving spherical averages, which were obtained in [
References:
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Y. Cho, Z. Guo and S. Lee,
A Sobolev estimate for the adjoint restriction operator, Math. Ann., 362 (2015), 799-815.
doi: 10.1007/s00208-014-1130-7. |
| [2] |
Y. Cho and S. Lee,
Strichartz estimates in spherical coordinates, Indiana Univ. Math. J., 62 (2013), 991-1020.
doi: 10.1512/iumj.2013.62.4970. |
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Y. Cho, T. Ozawa and S. Xia,
Remarks on some dispersive estimates, Commun. Pure Appl. Anal., 10 (2011), 1121-1128.
doi: 10.3934/cpaa.2011.10.1121. |
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D. Fang and C. Wang,
Weighted Strichartz estimates with angular regularity and their applications, Forum Math., 23 (2011), 181-205.
doi: 10.1515/FORM.2011.009. |
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Z. Guo,
Sharp spherically averaged Stichartz estimates for the Schrödinger equation, Nonlinearity, 29 (2016), 1668-1686.
doi: 10.1088/0951-7715/29/5/1668. |
| [6] |
Z. Guo and Y. Wang,
Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations, J. Anal. Math., 124 (2014), 1-38.
doi: 10.1007/s11854-014-0025-6. |
| [7] |
J.-C. Jiang, C. Wang and X. Yu,
Generalized and weighted Strichartz estimates, Commun. Pure Appl. Anal., 11 (2012), 1723-1752.
doi: 10.3934/cpaa.2012.11.1723. |
| [8] |
M. Keel and T. Tao,
Endpoint Strichartz estimates, Amer. J. Math., 120 (1998), 955-980.
|
| [9] |
J. Sterbenz,
Angular regularity and Strichartz estimates for the wave equation, Int. Math. Res. Not., (), 187-231.
doi: 10.1155/IMRN.2005.187. |
| [10] |
R. S. Strichartz,
Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J., 44 (1977), 705-714.
|
show all references
References:
| [1] |
Y. Cho, Z. Guo and S. Lee,
A Sobolev estimate for the adjoint restriction operator, Math. Ann., 362 (2015), 799-815.
doi: 10.1007/s00208-014-1130-7. |
| [2] |
Y. Cho and S. Lee,
Strichartz estimates in spherical coordinates, Indiana Univ. Math. J., 62 (2013), 991-1020.
doi: 10.1512/iumj.2013.62.4970. |
| [3] |
Y. Cho, T. Ozawa and S. Xia,
Remarks on some dispersive estimates, Commun. Pure Appl. Anal., 10 (2011), 1121-1128.
doi: 10.3934/cpaa.2011.10.1121. |
| [4] |
D. Fang and C. Wang,
Weighted Strichartz estimates with angular regularity and their applications, Forum Math., 23 (2011), 181-205.
doi: 10.1515/FORM.2011.009. |
| [5] |
Z. Guo,
Sharp spherically averaged Stichartz estimates for the Schrödinger equation, Nonlinearity, 29 (2016), 1668-1686.
doi: 10.1088/0951-7715/29/5/1668. |
| [6] |
Z. Guo and Y. Wang,
Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations, J. Anal. Math., 124 (2014), 1-38.
doi: 10.1007/s11854-014-0025-6. |
| [7] |
J.-C. Jiang, C. Wang and X. Yu,
Generalized and weighted Strichartz estimates, Commun. Pure Appl. Anal., 11 (2012), 1723-1752.
doi: 10.3934/cpaa.2012.11.1723. |
| [8] |
M. Keel and T. Tao,
Endpoint Strichartz estimates, Amer. J. Math., 120 (1998), 955-980.
|
| [9] |
J. Sterbenz,
Angular regularity and Strichartz estimates for the wave equation, Int. Math. Res. Not., (), 187-231.
doi: 10.1155/IMRN.2005.187. |
| [10] |
R. S. Strichartz,
Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J., 44 (1977), 705-714.
|
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