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Daniel Spirn

School of Mathematics
University of Minnesota


Vincent Hall 508


(612) 625-1349
(612) 625-2004
(612) 626-2017



PDE Seminar

Wednesdays, 3:35--4:35 PM.

Research Interests

Partial Differential Equations, Applied Mathematics.


Gross-Pitaevskii vortex motion with critically-scaled inhomogeneities with M. Kurzke, J. Marzuola, 31 pages, submitted. pdf

Petviashvilli's Method for the Dirichlet Problem with D. Olson, S. Shukla, and G. Simpson, 21 pages, J. Scientific Comp. 66 (2016) 296--320. pdf

Recovering a Potential from Cauchy Data via Complex Geometric Optics Solutions with H.-M. Nguyen, 33 pages. pdf

Hydrodynamic limit of the Gross-Pitaevsky equation with R.Jerrard, Comm. Parial Differential Equations 40 (2015) 135--190. pdf

Vortex liquids and the Ginzburg-Landau equation with M. Kurzke, Forum Math. Sigma 2 (2015) 135--190. pdf

Exploring Vortex Dynamics in the Presence of Dissipation: Analytical and Numerical Results with D. Yan, R. Carretero-Gonzalez, D.J.Frantzeskakis, P.G. Keverekidis, N.P Proukakis, Physical Rev. A 89 (2014) 043613-1. pdf

Vortex dynamics in the presence of excess energy for the Landau-Lifschitz-Gilbert equation with M. Kurzke, C. Melcher, and R. Moser, Calc. Var. Partial Differential Equations 49 (2014) 1019-1043. pdf

On the regularity of the flow map for the gravity-capillary equations with R.M. Chen, J. Marzuola, and J.D. Wright, J. Funct. Anal. 264 (2013) 752--782. pdf

Asymptotic behavior and symmetry of condensate solutions in electroweak theory with R.M. Chen and Y.J. Guo, J. Anal. Math. 117 (2012) 47--85. pdf

Gamma stability and vortex motion in type II superconductors with M. Kurzke, Comm. Partial Differential Equations 36 (2011) 256--292. pdf

Ginzburg-Landau vortices driven by the Landau-Lifschetz-Gilbert equations with M. Kurzke, C. Melcher, and R. Moser, Arch. Ration. Mech. Anal. 199 (2011) 843--888. pdf

Quantitative equipartition of the Ginzburg-Landau energy with applications with M. Kurzke, Indiana U. J. Math. 59 (2010) 2077--2092. pdf

Linear dispersive decay estimates for the 3+1 dimensional water wave equation with surface tension with D. Wright, Can. Math. Bull. 55 (2012) 176--187. pdf

Dynamics of Ginzburg-Landau vortices in a mixed flow with M. Kurzke, C. Melcher, and R. Moser, Indiana U. J. Math. 58 (2009), 2597--2621. pdf

Electrically and magnetically charged vortices in the Chern-Simons-Higgs theory with R.M. Chen, Y.J. Guo, and Y. Yang, Proc. Royal Soc. London Ser. A. 465 (2009), 3489--3516. pdf

Uniqueness of stable Meissner state solutions of the Chern-Simons-Higgs energy  with X. Yan, ESAIM: COCV16 (2010), 23--36. pdf

Minimizers of the nonself-dual Chern-Simons-Higgs energy near the first critical field  with X. Yan, Calc. Var. Partial Differential Equations 35 (2009), 1--37. pdf

Linear dispersive decay estimates for vortex sheets with surface tension with D. Wright, Comm. Math. Sci. 7 (2009), 521--547. pdf

Symmetric Chern-Simons-Higgs vortices with R.M. Chen, Comm. Math. Phys. 285 (2009), 1005--1031. pdf

On the energy of superconductors in large and small domains with M. Kurzke, SIAM J. Math. Anal. 40 (2009), 2077--2104. pdf

On the energy of a Chern-Simons-Higgs vortex lattice with M. Kurzke, CRM Proceedings and Lecture Notes 44 (2008), 127--152. pdf

Scaling limits of the Chern-Simons-Higgs energy with M. Kurzke, Commun. Contemp. Math. 10 (2008), 1--16. pdf

Gamma-Limit of the nonself-dual Chern-Simons-Higgs energy with M. Kurzke, J. Funct. Anal. 244 (2008), 535--588. pdf

Dynamics near unstable interfacial fluids with Y. Guo and C. Hallstrom, Comm. Math. Phys. 270 (2007), 635--689. pdf

Refined Jacobian estimates and the Gross-Pitaevsky equations with R. Jerrard, Arch. Ration. Mech. Anal. 190 (2008), 425--475. pdf

Refined Jacobian estimates for the Ginzburg-Landau functional with R. Jerrard,  Indiana U. J. Math. 56 (2007), 135--186. pdf

Dynamics Near an Unstable Kirchhoff Ellipse with Y. Guo and C. Hallstrom, Comm. Math. Phys. 245 (2004), 297--354. pdf

Vortex motion laws for the Schrödinger-Ginzburg-Landau equations, SIAM J. Math. Anal. 43 (2003), 1435--1476. pdf

Vortex dynamics of the full time-dependent Ginzburg-Landau equations, Comm. Pure Appl. Math. 55 (2002), no. 5, 537--581.

A two-dimensional model for slow convection at infinite Marangoni number with A. Thess and B. Juettner, J. Fluid Mech. 331 (1997), 283--312.

Viscous flow at infinite Marangoni number with A. Thess and B. Juettner, Phys. Rev. Lett. 75 (1995), no. 25, 4614--4617.