Hello! Welcome to my website.
My name is Akansha Sanwal, and I am a postdoctoral researcher at Innsbruck University. My mentor is Prof. Birgit Schoerkhuber.
My area of research is nonlinear dispersive equations. I work on questions related to well-posedness and stability of solutions to these equations.
October 2018-October 2022, PhD, Bielefeld University, Germany. (Supervisor: Sebastian Herr)
July 2016-June 2018, Master's, Indian Institute of Technology (IIT) Roorkee, India.
July 2013-June 2016, Bachelor's, Delhi University, India.
1) Sharp local well-posedness for KP-I equations in the semilinear regime (with S. Kinoshita and R. Schippa) (Under revision)
2) Improved well-posedness for dispersion-generalized KP-I equations in the quasilinear regime (with S. Kinoshita and R. Schippa), Discrete and Continuous Dynamical Systems, 45.10 (2025): 3625-3661.
3) Low regularity well-posedness of KP-I equations: the three-dimensional case (with S. Herr and R. Schippa), Journal of Functional Analysis, 2024, Volume 286, Issue 4.
4) Decoupling inequality for paraboloid under shell type restriction and its application to the periodic Zakharov system (with S. Kinoshita and S. Nakamura), Communications in Mathematical Physics.
5) Low regularity well-posedness for KP-I equations: the dispersion generalised case (with R. Schippa), Nonlinearity, 2023, 36 4342. doi: 10.1088/1361-6544/ace1cc.
6) Local well-posedness for the Zakharov system in dimension d <=3, Discrete and Continuous Dynamical Systems, 2022, 42 (3) : 1067-1103. doi: 10.3934/dcds.2021147.
At Innsbruck University, I have taught Analysis 1, Analysis 2 and Linear Algebra as a Teaching Assistant. I am currently a lecturer for "Advanced Topics in PDEs", which I share with Prof. Schoerkhuber.
Previously, at Bielefeld University, I was a tutor for Analysis 2, Complex Analysis, Partial Differential Equations 1, Partial Differential Equations 2, Optimisation and Dynamics, and Functional Analysis.
"Well-posedness for the dispersion-generalised KP-I equations", October 2024, Bernoulli Workshop: Young researchers in deterministic and probabilistic dispersive equations, EPFL, Lausanne, Switzerland. (invited)
"Low regularity well-posedness for nonlinear dispersive equations", February 2024, Analysis seminar, Harish-Chandra Research Institute, Prayagraj, India. (invited)
"Low regularity well-posedness for dispersion generalised KP-I equations", March 2023, Analysis and PDE seminar, Innsbruck University, Innsbruck, Austria.
"Low regularity well-posedness for dispersion generalised KP-I equations", February 2023, Women in nonlinear dispersive PDEs, BIRS Banff, Canada. (invited)
"Local well-posedness for the Zakharov system in dimension d <=3", June 2021, KIAS Analysis & PDE seminar, Seoul, South Korea.
"Local well-posedness for the Zakharov system in dimension d <=3", April 2021, Analysis seminar, Bielefeld, Germany.
"Non-linear Schrödinger equation: Local theory", October 2020, BGTS Doctoral Day, Bielefeld, Germany.
As part of the doctoral programme IRTG 2235, I visited the Korea Advanced Institute of Science and Technology (KAIST) in Daejeon, South Korea, in 2021. My host there was Prof. Soonsik Kwon.
I was born in the Himalayan state of Uttarakhand in India (see a picture of the Panchachuli range of the Himalayas above).
In my free time, I like to scribble. I also enjoy playing badminton.