Yilun (Allen) Wu

Curriculum Vitae:

Curriculum Vitae

Research Statement:

Research Statement

Current Projects:

  1. The direct scattering problem of the Intermediate Long Wave equation
    (with Peter Perry).

    Abstract: This is a project to explore the complete integrability of the Intermediate Long Wave (ILW) Equation, which is a model of internal gravity waves in a two layer fluid. The ILW equation is an equation to bridge between the Kortweg-deVries equation and the Benjamin-Ono equation.

  2. The Inverse scattering problem of the Benjamin-Ono equation

    Abstract: This is a project to study the large data inverse scattering problem of the Benjamin-Ono equation. This will rigorously establish the complete integrability in a more general setting than is currently available in the literature.

  3. The stability of disc galaxies
    (with Walter Strauss).

    Abstract: This is a project to study fluid and kinetic models of 2D galaxies. Existence and stability of rotating solutions are explored.

  4. Global continuation of surface waves on a 2D droplet
    (with Gary Moon).

    Abstract: This is a project to construct steady surface capillary waves on a 2D droplet of water. Local and global continuation results will be proven.

Reprints and Preprints:

  1. Global Continuation of a Vlasov Model of Rotating Galaxies
    (with Walter Strauss), accepted by Kinetic and Related Models.

  2. Existence of Rotating Stars with Variable Entropy
    (with Juhi Jang and Walter Strauss), accepted by SIAM Journal of Mathematical Analysis.

  3. Rapidly Rotating White Dwarfs
    (with Walter Strauss), Nonlinearity, 33.9 (2020): 4783.

  4. Global Continuation and the Theory of Rotating Stars
    Quarterly of Applied Mathematics, 78.1 (2020): 147-159.

  5. Rapidly Rotating Stars
    (with Walter Strauss), Communications in Mathematical Physics, 368 (2020): 701-721.

  6. Existence of Rotating Magnetic Stars
    (with Juhi Jang and Walter Strauss), Phyisica D: Nonlinear Phenomena 397 (2019): 65-74.

  7. Steady States of Rotating Stars and Galaxies
    (with Walter Strauss), SIAM Journal on Mathematical Analysis 49.6 (2017): 4865-4914.

  8. Jost Solutions and the Direct Scattering Problem of the Benjamin-Ono Equation
    SIAM Journal on Mathematical Analysis 49.6 (2017): 5158-5206.

  9. Simplicity and Finiteness of Discrete Spectrum of the Benjamin-Ono Scattering Operator
    SIAM Journal on Mathematical Analysis 48.2 (2016): 1348-1367.

  10. Existence of rotating planet solutions to the Euler-Poisson equations with an inner hard core
    Archive for Rational Mechanics and Analysis 219 (2016): 1-26.

  11. On rotating star solutions to the non-isentropic Euler-Poisson equations
    Journal of Differential Equations 259.12 (2015): 7161-7198.