Contact Information.
 Office: 313 Rolla Building
 Phone: (573) 3414654
 Email: jason (dot) murphy (at) mst (dot) edu
Curriculum Vitae.
 Education:
 B.S. Mathematics, UT Austin 2009
 M.A. Mathematics, UCLA 2010
 Ph.D. Mathematics, UCLA 2014
 Academic Positions:
 NSF Postdoctoral Fellow, UC Berkeley 2014–2017
 Assistant Professor, Missouri S&T 2017–present
For a complete CV, click here.
Department of Mathematics and Statistics
Missouri University of Science and Technology
My research is in the area of harmonic analysis and nonlinear partial differential equations, with an emphasis on the longtime behavior of solutions to nonlinear dispersive equations.
Profiles
Preprints
 Failure of scattering to solitary waves for longrange nonlinear Schrödinger equations.
Joint with K. Nakanishi.
[arXiv]
 Scattering below the ground state for the 2d radial nonlinear Schrödinger equation.
Joint with A. Arora and B. Dodson.
[arXiv]
 Numerical simulations for the energysupercritical nonlinear wave equation.
Joint with Y. Zhang.
[arXiv]
 Invariance of white noise for KdV on the line.
Joint with R. Killip and M. Visan.
[arXiv]
 Scattering for defocusing energy subcritical nonlinear wave equations.
Joint with B. Dodson, A. Lawrie, and D. Mendelson.
[arXiv]
 The energycritical nonlinear wave equation with an inversesquare potential.
Joint with C. Miao and J. Zheng.
[arXiv]
 Stability of small solitary waves for the 1d NLS with an attractive delta potential.
Joint with S. Masaki and J. Segata.
To appear in Anal. PDE.
[arXiv]
Publications
 Modified scattering for the onedimensional cubic NLS with a repulsive delta potential.
Joint with S. Masaki and J. Segata.
To appear in Int. Math. Res. Not.
[arXiv]
[Journal]
 Almost sure scattering for the energycritical NLS with radial data
below H^{1}(R^{4}).
Joint with R. Killip and M. Visan.
Comm. Partial Differential Equations 44 (2019), no. 1, 51–71.
[arXiv] [Journal] [MathSciNet]
 The nonlinear Schrödinger equation with an inversesquare potential.
Contemporary Mathematics, 725 (2019)
[pdf] [Journal] [MathSciNet]
 The radial masssubcritical NLS in negative order Sobolev spaces.
Joint with R. Killip, S. Masaki, and M. Visan.
Discrete Contin. Dyn. Syst. SeriesA 39 (2019), no. 1, 553–583.
[arXiv] [Journal] [MathSciNet]
 Random data finalstate problem for the masssubcritical NLS in L^{2}.
Proc. Amer. Math. Soc. 147 (2019), no. 1, 339–350.
[arXiv] [Journal] [MathSciNet]
 A new proof of scattering below the ground state for the nonradial focusing NLS.
Joint with B. Dodson.
Math. Res. Lett. 25 (2018), no. 6, 1805–1825.
[arXiv] [Journal] [MathSciNet]
 The initialvalue problem for the cubicquintic NLS with nonvanishing boundary conditions.
Joint with R. Killip and M. Visan.
SIAM J. Math. Anal. 50 (2018), no. 3, 2681–2739.
[arXiv] [Journal] [MathSciNet]
 Scattering in H^{1} for the intercritical NLS with an inversesquare potential.
Joint with J. Lu and C. Miao.
J. Differential Equations 264 (2018), no. 5, 3174–3211.
[arXiv]
[Journal] [MathSciNet]
 A new proof of scattering below the ground state for the 3d radial focusing cubic NLS.
Joint with B. Dodson.
Proc. Amer. Math. Soc. 145 (2017), no. 11, 4859–4867.
[arXiv]
[Journal]
[MathSciNet]
 Large data masssubcritical NLS: critical weighted bounds imply scattering.
Joint with R. Killip, S. Masaki, and M. Visan.
NoDEA Nonlinear Differential Equations Appl. 24 (2017), no. 4, Art. 38, 33pp.
[arXiv] [Journal] [MathSciNet]
 Almost global existence for cubic nonlinear Schrödinger equations in one space dimension.
Joint with F. Pusateri.
Discrete Contin. Dyn. Syst. SeriesA 37 (2017), 2077–2102.
[arXiv]
[Journal]
[MathSciNet]
 The focusing cubic NLS with inversesquare potential in three space dimensions.
Joint with R. Killip, M. Visan, and J. Zheng.
Differential Integral Equations 30 (2017), no. 34, 161–206.
[arXiv]
[Journal]
[MathSciNet]
 The defocusing quintic NLS in four space dimensions.
Joint with B. Dodson, C. Miao, and J. Zheng.
Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 3, 759–787.
[arXiv]
[Journal] [MathSciNet]
 The finalstate problem for the cubicquintic NLS with nonvanishing boundary conditions.
Joint with R. Killip and M. Visan.
Anal. PDE 9 (2016), no. 7, 1523–1574.
[arXiv]
[Journal]
[MathSciNet]
 The radial defocusing nonlinear Schrödinger equation in three space dimensions.
Comm. Partial Differential Equations 40 (2015), no. 2, 265–308.
[arXiv]
[Journal]
[MathSciNet]
 The defocusing energysupercritical NLS in four space dimensions.
Joint with C. Miao and J. Zheng.
J. Funct. Anal. 267 (2014), no. 6, 1662–1724.
[arXiv]
[Journal]
[MathSciNet]
 The defocusing H^{1/2}critical NLS in high dimensions.
Discrete Contin. Dyn. Syst. SeriesA 34 (2014), no. 2, 733–748.
[arXiv]
[Journal]
[MathSciNet]
 Intercritical NLS: critical H^{s}bounds imply scattering.
SIAM J. Math. Anal. 46 (2014), no. 1, 939–997.
[arXiv]
[Journal]
[MathSciNet]
Other
 Subcritical scattering for defocusing nonlinear Schrödinger equations.
Expository paper. [pdf]
 Nonlinear Schrödinger equations at nonconserved critical regularity.
Ph.D. Thesis (2014)
[pdf]
[MathSciNet]
Past Collaborators
Fall 2019 Teaching:
 Math 3108103  Linear Algebra
 Lecture: MWF 1pm1:50pm (Emerson Electric Co. G31)
 Math 5215101  Introduction to Real Analysis
 Lecture: MWF 3pm3:50pm (Rolla G4)
 Office Hours: MWF 2pm2:50pm (Rolla 313)
 Websites through Canvas.
Past Teaching:
Missouri S&T (2017present)
 Summer 2019: Math 3304  Differential Equations
 Spring 2019: Math 6462  Harmonic Analysis II
 Fall 2018:
 Math 3108A  Linear Algebra
 Math 6461  Harmonic Analysis I
 Spring 2018: Math 5215  Introduction to Real Analysis
 Fall 2017: Math 3108AB  Linear Algebra
University of California, Berkeley (20142017)
 Spring 2017: Math 121B  Mathematical Tools for the Physical Sciences
 Fall 2016: Math 204  Ordinary Differential Equations
 Spring 2015: Math 185  Complex Analysis
 Fall 2014: Math 126  Partial Differential Equations
Lecture Notes:
 Harmonic Analysis.
Lecture Notes for Math 6461 and 6462 at Missouri S&T. [pdf] [link]
 Introduction to Real Analysis.
Lecture Notes for Math 5215 at Missouri S&T. [pdf]
 Linear Algebra.
Lecture Slides for Math 3108 at Missouri S&T. [pdf]
 Introduction to Complex Analysis.
Lecture Notes for Math 185 at UC Berkeley. [pdf]
 Introduction to Partial Differential Equations.
Lecture Notes for Math 126 at UC Berkeley. [pdf]
