On the Critical Norm Concentration for the Inhomogeneous Nonlinear Schrödinger Equation
Abstract We consider the inhomogeneous nonlinear Schrödinger equation (INLS) in $${\mathbb {R}}^N$$i∂tu+Δu+|x|-b|u|2σu=0,$$\begin{aligned} i \partial _t u + \Delta u + |x|^{-b} |u|^{2\sigma }u = 0, \end{aligned}$$and show the $$L^2$$-norm concentration for the finite time blow-up solutions in the $$...
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| Autor*in: |
Campos, Luccas [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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Enthalten in: Journal of dynamics and differential equations - Springer US, 1989, 34(2022), 3 vom: 24. März, Seite 2347-2369 |
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volume:34 ; year:2022 ; number:3 ; day:24 ; month:03 ; pages:2347-2369 |
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| DOI / URN: |
10.1007/s10884-022-10151-4 |
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OLC2079523945 |
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| 520 | |a Abstract We consider the inhomogeneous nonlinear Schrödinger equation (INLS) in $${\mathbb {R}}^N$$i∂tu+Δu+|x|-b|u|2σu=0,$$\begin{aligned} i \partial _t u + \Delta u + |x|^{-b} |u|^{2\sigma }u = 0, \end{aligned}$$and show the $$L^2$$-norm concentration for the finite time blow-up solutions in the $$L^2$$-critical case, $$\sigma =\frac{2-b}{N}$$. Moreover, we provide an alternative proof for the classification of minimal mass blow-up solutions, first proved by Genoud and Combet (J Evol Equ 16(2):483–500, 2016, https://doi.org/10.1007/s00028-015-0309-z). For the case $$\frac{2-b}{N}< \sigma < \frac{2-b}{N-2}$$, we show results regarding the $$L^p$$-critical norm concentration, generalizing the argument of Holmer and Roudenko (Appl Math Res eXpress 2007(1):Art. ID abm004, 2007) to the INLS setting. | ||
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10.1007/s10884-022-10151-4 doi (DE-627)OLC2079523945 (DE-He213)s10884-022-10151-4-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Campos, Luccas verfasserin aut On the Critical Norm Concentration for the Inhomogeneous Nonlinear Schrödinger Equation 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We consider the inhomogeneous nonlinear Schrödinger equation (INLS) in $${\mathbb {R}}^N$$i∂tu+Δu+|x|-b|u|2σu=0,$$\begin{aligned} i \partial _t u + \Delta u + |x|^{-b} |u|^{2\sigma }u = 0, \end{aligned}$$and show the $$L^2$$-norm concentration for the finite time blow-up solutions in the $$L^2$$-critical case, $$\sigma =\frac{2-b}{N}$$. Moreover, we provide an alternative proof for the classification of minimal mass blow-up solutions, first proved by Genoud and Combet (J Evol Equ 16(2):483–500, 2016, https://doi.org/10.1007/s00028-015-0309-z). For the case $$\frac{2-b}{N}< \sigma < \frac{2-b}{N-2}$$, we show results regarding the $$L^p$$-critical norm concentration, generalizing the argument of Holmer and Roudenko (Appl Math Res eXpress 2007(1):Art. ID abm004, 2007) to the INLS setting. Inhomogeneous nonlinear Schrödinger equation Mass concentration Critical norm concentration Concentration-compactness Cardoso, Mykael (orcid)0000-0001-9990-7400 aut Enthalten in Journal of dynamics and differential equations Springer US, 1989 34(2022), 3 vom: 24. März, Seite 2347-2369 (DE-627)165666455 (DE-600)1008261-X (DE-576)023042591 1040-7294 nnns volume:34 year:2022 number:3 day:24 month:03 pages:2347-2369 https://doi.org/10.1007/s10884-022-10151-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 34 2022 3 24 03 2347-2369 |
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10.1007/s10884-022-10151-4 doi (DE-627)OLC2079523945 (DE-He213)s10884-022-10151-4-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Campos, Luccas verfasserin aut On the Critical Norm Concentration for the Inhomogeneous Nonlinear Schrödinger Equation 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We consider the inhomogeneous nonlinear Schrödinger equation (INLS) in $${\mathbb {R}}^N$$i∂tu+Δu+|x|-b|u|2σu=0,$$\begin{aligned} i \partial _t u + \Delta u + |x|^{-b} |u|^{2\sigma }u = 0, \end{aligned}$$and show the $$L^2$$-norm concentration for the finite time blow-up solutions in the $$L^2$$-critical case, $$\sigma =\frac{2-b}{N}$$. Moreover, we provide an alternative proof for the classification of minimal mass blow-up solutions, first proved by Genoud and Combet (J Evol Equ 16(2):483–500, 2016, https://doi.org/10.1007/s00028-015-0309-z). For the case $$\frac{2-b}{N}< \sigma < \frac{2-b}{N-2}$$, we show results regarding the $$L^p$$-critical norm concentration, generalizing the argument of Holmer and Roudenko (Appl Math Res eXpress 2007(1):Art. ID abm004, 2007) to the INLS setting. Inhomogeneous nonlinear Schrödinger equation Mass concentration Critical norm concentration Concentration-compactness Cardoso, Mykael (orcid)0000-0001-9990-7400 aut Enthalten in Journal of dynamics and differential equations Springer US, 1989 34(2022), 3 vom: 24. März, Seite 2347-2369 (DE-627)165666455 (DE-600)1008261-X (DE-576)023042591 1040-7294 nnns volume:34 year:2022 number:3 day:24 month:03 pages:2347-2369 https://doi.org/10.1007/s10884-022-10151-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 34 2022 3 24 03 2347-2369 |
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10.1007/s10884-022-10151-4 doi (DE-627)OLC2079523945 (DE-He213)s10884-022-10151-4-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Campos, Luccas verfasserin aut On the Critical Norm Concentration for the Inhomogeneous Nonlinear Schrödinger Equation 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We consider the inhomogeneous nonlinear Schrödinger equation (INLS) in $${\mathbb {R}}^N$$i∂tu+Δu+|x|-b|u|2σu=0,$$\begin{aligned} i \partial _t u + \Delta u + |x|^{-b} |u|^{2\sigma }u = 0, \end{aligned}$$and show the $$L^2$$-norm concentration for the finite time blow-up solutions in the $$L^2$$-critical case, $$\sigma =\frac{2-b}{N}$$. Moreover, we provide an alternative proof for the classification of minimal mass blow-up solutions, first proved by Genoud and Combet (J Evol Equ 16(2):483–500, 2016, https://doi.org/10.1007/s00028-015-0309-z). For the case $$\frac{2-b}{N}< \sigma < \frac{2-b}{N-2}$$, we show results regarding the $$L^p$$-critical norm concentration, generalizing the argument of Holmer and Roudenko (Appl Math Res eXpress 2007(1):Art. ID abm004, 2007) to the INLS setting. Inhomogeneous nonlinear Schrödinger equation Mass concentration Critical norm concentration Concentration-compactness Cardoso, Mykael (orcid)0000-0001-9990-7400 aut Enthalten in Journal of dynamics and differential equations Springer US, 1989 34(2022), 3 vom: 24. März, Seite 2347-2369 (DE-627)165666455 (DE-600)1008261-X (DE-576)023042591 1040-7294 nnns volume:34 year:2022 number:3 day:24 month:03 pages:2347-2369 https://doi.org/10.1007/s10884-022-10151-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 34 2022 3 24 03 2347-2369 |
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10.1007/s10884-022-10151-4 doi (DE-627)OLC2079523945 (DE-He213)s10884-022-10151-4-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Campos, Luccas verfasserin aut On the Critical Norm Concentration for the Inhomogeneous Nonlinear Schrödinger Equation 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We consider the inhomogeneous nonlinear Schrödinger equation (INLS) in $${\mathbb {R}}^N$$i∂tu+Δu+|x|-b|u|2σu=0,$$\begin{aligned} i \partial _t u + \Delta u + |x|^{-b} |u|^{2\sigma }u = 0, \end{aligned}$$and show the $$L^2$$-norm concentration for the finite time blow-up solutions in the $$L^2$$-critical case, $$\sigma =\frac{2-b}{N}$$. Moreover, we provide an alternative proof for the classification of minimal mass blow-up solutions, first proved by Genoud and Combet (J Evol Equ 16(2):483–500, 2016, https://doi.org/10.1007/s00028-015-0309-z). For the case $$\frac{2-b}{N}< \sigma < \frac{2-b}{N-2}$$, we show results regarding the $$L^p$$-critical norm concentration, generalizing the argument of Holmer and Roudenko (Appl Math Res eXpress 2007(1):Art. ID abm004, 2007) to the INLS setting. Inhomogeneous nonlinear Schrödinger equation Mass concentration Critical norm concentration Concentration-compactness Cardoso, Mykael (orcid)0000-0001-9990-7400 aut Enthalten in Journal of dynamics and differential equations Springer US, 1989 34(2022), 3 vom: 24. März, Seite 2347-2369 (DE-627)165666455 (DE-600)1008261-X (DE-576)023042591 1040-7294 nnns volume:34 year:2022 number:3 day:24 month:03 pages:2347-2369 https://doi.org/10.1007/s10884-022-10151-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 34 2022 3 24 03 2347-2369 |
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10.1007/s10884-022-10151-4 doi (DE-627)OLC2079523945 (DE-He213)s10884-022-10151-4-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Campos, Luccas verfasserin aut On the Critical Norm Concentration for the Inhomogeneous Nonlinear Schrödinger Equation 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We consider the inhomogeneous nonlinear Schrödinger equation (INLS) in $${\mathbb {R}}^N$$i∂tu+Δu+|x|-b|u|2σu=0,$$\begin{aligned} i \partial _t u + \Delta u + |x|^{-b} |u|^{2\sigma }u = 0, \end{aligned}$$and show the $$L^2$$-norm concentration for the finite time blow-up solutions in the $$L^2$$-critical case, $$\sigma =\frac{2-b}{N}$$. Moreover, we provide an alternative proof for the classification of minimal mass blow-up solutions, first proved by Genoud and Combet (J Evol Equ 16(2):483–500, 2016, https://doi.org/10.1007/s00028-015-0309-z). For the case $$\frac{2-b}{N}< \sigma < \frac{2-b}{N-2}$$, we show results regarding the $$L^p$$-critical norm concentration, generalizing the argument of Holmer and Roudenko (Appl Math Res eXpress 2007(1):Art. ID abm004, 2007) to the INLS setting. Inhomogeneous nonlinear Schrödinger equation Mass concentration Critical norm concentration Concentration-compactness Cardoso, Mykael (orcid)0000-0001-9990-7400 aut Enthalten in Journal of dynamics and differential equations Springer US, 1989 34(2022), 3 vom: 24. März, Seite 2347-2369 (DE-627)165666455 (DE-600)1008261-X (DE-576)023042591 1040-7294 nnns volume:34 year:2022 number:3 day:24 month:03 pages:2347-2369 https://doi.org/10.1007/s10884-022-10151-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 34 2022 3 24 03 2347-2369 |
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On the Critical Norm Concentration for the Inhomogeneous Nonlinear Schrödinger Equation |
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Abstract We consider the inhomogeneous nonlinear Schrödinger equation (INLS) in $${\mathbb {R}}^N$$i∂tu+Δu+|x|-b|u|2σu=0,$$\begin{aligned} i \partial _t u + \Delta u + |x|^{-b} |u|^{2\sigma }u = 0, \end{aligned}$$and show the $$L^2$$-norm concentration for the finite time blow-up solutions in the $$L^2$$-critical case, $$\sigma =\frac{2-b}{N}$$. Moreover, we provide an alternative proof for the classification of minimal mass blow-up solutions, first proved by Genoud and Combet (J Evol Equ 16(2):483–500, 2016, https://doi.org/10.1007/s00028-015-0309-z). For the case $$\frac{2-b}{N}< \sigma < \frac{2-b}{N-2}$$, we show results regarding the $$L^p$$-critical norm concentration, generalizing the argument of Holmer and Roudenko (Appl Math Res eXpress 2007(1):Art. ID abm004, 2007) to the INLS setting. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
| abstractGer |
Abstract We consider the inhomogeneous nonlinear Schrödinger equation (INLS) in $${\mathbb {R}}^N$$i∂tu+Δu+|x|-b|u|2σu=0,$$\begin{aligned} i \partial _t u + \Delta u + |x|^{-b} |u|^{2\sigma }u = 0, \end{aligned}$$and show the $$L^2$$-norm concentration for the finite time blow-up solutions in the $$L^2$$-critical case, $$\sigma =\frac{2-b}{N}$$. Moreover, we provide an alternative proof for the classification of minimal mass blow-up solutions, first proved by Genoud and Combet (J Evol Equ 16(2):483–500, 2016, https://doi.org/10.1007/s00028-015-0309-z). For the case $$\frac{2-b}{N}< \sigma < \frac{2-b}{N-2}$$, we show results regarding the $$L^p$$-critical norm concentration, generalizing the argument of Holmer and Roudenko (Appl Math Res eXpress 2007(1):Art. ID abm004, 2007) to the INLS setting. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
| abstract_unstemmed |
Abstract We consider the inhomogeneous nonlinear Schrödinger equation (INLS) in $${\mathbb {R}}^N$$i∂tu+Δu+|x|-b|u|2σu=0,$$\begin{aligned} i \partial _t u + \Delta u + |x|^{-b} |u|^{2\sigma }u = 0, \end{aligned}$$and show the $$L^2$$-norm concentration for the finite time blow-up solutions in the $$L^2$$-critical case, $$\sigma =\frac{2-b}{N}$$. Moreover, we provide an alternative proof for the classification of minimal mass blow-up solutions, first proved by Genoud and Combet (J Evol Equ 16(2):483–500, 2016, https://doi.org/10.1007/s00028-015-0309-z). For the case $$\frac{2-b}{N}< \sigma < \frac{2-b}{N-2}$$, we show results regarding the $$L^p$$-critical norm concentration, generalizing the argument of Holmer and Roudenko (Appl Math Res eXpress 2007(1):Art. ID abm004, 2007) to the INLS setting. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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| title_short |
On the Critical Norm Concentration for the Inhomogeneous Nonlinear Schrödinger Equation |
| url |
https://doi.org/10.1007/s10884-022-10151-4 |
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| author2 |
Cardoso, Mykael |
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Cardoso, Mykael |
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| doi_str |
10.1007/s10884-022-10151-4 |
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2024-07-04T01:14:18.608Z |
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