This paper is concerned with the Cauchy problem of the 2D Zakharov-Kuznetsov equation.
We prove bilinear estimates which imply local in time well-posedness in the Sobolev space …

We prove local in time well-posedness for the Zakharov system in two space dimensions
with large initial data in L 2× H− 1/2× H− 3/2. This is the space of optimal regularity in the …

We prove low regularity global well-posedness for the 1d Zakharov system and the 3d Klein-
Gordon-Schrödinger system, which are systems in two variables $ u:\mathbb {R} _x …

In this paper we prove local well-posedness of a space-time fractional generalization of the
nonlinear Schrödinger equation with a power-type nonlinearity. The linear equation …

We completely determine the range of Sobolev regularity for the Dirac-Klein-Gordon system,
the quadratic nonlinear Dirac equations, and the wave-map equation to be well posed …

In this paper, we establish local well-posedness for the Zakharov system on T d, d≥ 3 in a
low regularity setting. Our result improves the work of Kishimoto (J Anal Math 119: 213–253 …

This paper is concerned with the Cauchy problem of the modified Zakharov-Kuznetsov
equation on Rd. If d ¼ 2, we prove the sharp estimate which implies local in time well …

In this paper, we consider the well-posedness for the Cauchy problem of the Kawahara
equation with low regularity data in the periodic case. We obtain the local well-posedness …

The sharp range of Sobolev spaces is determined in which the Cauchy problem for the
classical Zakharov system is well-posed, which includes existence of solutions, uniqueness …

The initial value problem of the Zakharov system on the two dimensional torus with general
period is shown to be locally well posed in the Sobolev spaces of optimal regularity …