Monica Vișan (born August 5, 1979, in Drobeta-Turnu Severin, Romania) is a Romanian mathematician at the University of California, Los Angeles who specializes in partial differential equations and is well known for her work on the nonlinear Schrödinger equation.

Vișan earned a bachelor's degree at the University of Bucharest in 2002.^[1] She became a student of Terence Tao at the University of California, Los Angeles (UCLA), where she completed her doctorate in 2006. Her dissertation was The Defocusing Energy-Critical Nonlinear Schrödinger Equation in Dimensions Five and Higher.^[1][2]

After postdoctoral research at the Institute for Advanced Study, Vișan became an assistant professor in the mathematics department at the University of Chicago in 2008. She returned to UCLA as a faculty member in 2009 and (keeping her appointment at UCLA) spent 2010–2011 as Harrington Faculty Fellow at the University of Texas at Austin.^[1]

Vișan won a Sloan Research Fellowship in 2010.^[3] She was elected as a Fellow of the American Mathematical Society in the 2024 class of fellows.^[4]

With Herbert Koch and Daniel Tătaru, Vișan is the author of the book Dispersive Equations and Nonlinear Waves: Generalized Korteweg–de Vries, Nonlinear Schrödinger, Wave and Schrödinger Maps (Birkhäuser/Springer, 2014).

Her research papers include:

• Ryckman, Eric; Vișan, Monica (2007), "Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in ${\displaystyle \mathbb {R} ^{1+4}}$", American Journal of Mathematics, 129 (1): 1–60, arXiv:math/0501462, doi:10.1353/ajm.2007.0004, MR 2288737, S2CID 19024265
• Vișan, Monica (2007), "The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions", Duke Mathematical Journal, 138 (2): 281–374, arXiv:math/0508298, doi:10.1215/S0012-7094-07-13825-0, MR 2318286, S2CID 2427673
• Tao, Terence; Vișan, Monica; Zhang, Xiaoyi (2007), "The nonlinear Schrödinger equation with combined power-type nonlinearities", Communications in Partial Differential Equations, 32 (7–9): 1281–1343, arXiv:math/0511070, doi:10.1080/03605300701588805, MR 2354495, S2CID 15109526
• Killip, Rowan; Tao, Terence; Vișan, Monica (2009), "The cubic nonlinear Schrödinger equation in two dimensions with radial data", Journal of the European Mathematical Society, 11 (6): 1203–1258, arXiv:0707.3188, doi:10.4171/JEMS/180, MR 2557134
• Killip, Rowan; Vişan, Monica (2010), "The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher", American Journal of Mathematics, 132 (2): 361–424, arXiv:0804.1018, doi:10.1353/ajm.0.0107, MR 2654778, S2CID 1068572
• Killip, Rowan; Vişan, Monica (2013), "Nonlinear Schrödinger equations at critical regularity" (PDF), Evolution equations, Clay Math. Proc., vol. 17, Amer. Math. Soc., Providence, RI, pp. 325–437, MR 3098643