More Like this

1. The J-equation and the supercritical deformed Hermitian–Yang–Mills equation

   https://doi.org/10.1007/s00222-021-01035-3  

   Chen, Gao (August 2021, Inventiones mathematicae)
2. An integral equation method for the Cahn-Hilliard equation in the wetting problem

   https://doi.org/10.1016/j.jcp.2020.109521  

   Wei, Xiaoyu; Jiang, Shidong; Klöckner, Andreas; Wang, Xiao-Ping (October 2020, Journal of Computational Physics)
3. On the nonlinear Dysthe equation

   https://doi.org/10.1016/j.na.2021.112292  

   Grande, Ricardo; Kurianski, Kristin M.; Staffilani, Gigliola (June 2021, Nonlinear Analysis)

   null (Ed.)
4. Derivation of the ion equation

   Grenier, E (March 2020, Quarterly of applied mathematics)

   We consider the classical Euler-Poisson system for electrons and ions, interacting through an electrostatic field. The mass ratio of an electron and an ion is small and we establish an asymptotic expansion of solutions, where the main term is obtained from a solution to a self-consistent equation involving only the ion variables. Moreover, on R^3, the validity of such an expansion is established even with \ill-prepared" Cauchy data, by including an additional initial layer correction. 

   more » « less
5. Derivation of the ion equation

   https://doi.org/https://doi.org/10.1090/qam/1558  

   E. Grenier, Y. Guo (September 2019, Quarterly of applied mathematics)

   We consider the classical Euler-Poisson system for electrons and ions, interacting through an electrostatic field. The mass ratio of an electron and an ion $$ m_e/M_i\ll 1$$ is small and we establish an asymptotic expansion of solutions, where the main term is obtained from a solution to a self-consistent equation involving only the ion variables. Moreover, on $$ \mathbb{R}^3$$, the validity of such an expansion is established even with ``ill-prepared'' Cauchy data, by including an additional initial layer correction. 

   more » « less