307 citations · 580 across the 47 of their papers we have counts for
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On well-posedness and blow-up in the generalized Hartree equation
Anudeep K. Arora, Svetlana Roudenko
We study the generalized Hartree equation, which is a nonlinear Schrödinger-type equation with a nonlocal potential $iu_t + Δu + (|x|^{-b} \ast |u|^p)|u|^{p-2}u=0, x \in \mathbb{R}…
Global well-posedness for low regularity data in the 2d modified Zakharov-Kuznetsov equation
Debdeep Bhattacharya, Luiz Gustavo Farah, Svetlana Roudenko
We consider the modified Zakharov-Kuznetsov (mZK) equation in two space dimensions in both focusing and defocusing cases. Using the -method, we prove the global well-posedness o…
Global behavior of solutions to the focusing generalized Hartree equation
Anudeep Kumar Arora, Svetlana Roudenko
We study the global behavior of solutions to the nonlinear generalized Hartree equation, where the nonlinearity is of the non-local type and is expressed as a convolution, $$ i u_t…