相关论文: Local well-posedness below the charge norm for the…
We prove that for sufficiently small initial displacements in some weighted Sobolev space, the Cauchy problem of the systems of incompressible isotropic elastodynamics in two space dimensions admits a uniqueness global classical solution.
We consider the Cauchy problem for an equation of the form \partial_t+\partial_x^3)u=F(u,u_x,u_{xx}) where F is a polynomial with no constant or linear terms and no quadratic uu_{xx} term. For a polynomial nonlinearity with no quadratic…
We consider the Cauchy problem of the two-dimensional Schr\"odinger-Poisson system in the energy class. Though the Newtonian potential diverges at the spatial infinity in the logarithmic order, global well-posedness is proven in both…
In this paper, we study the Cauchy problem of the 3-dimensional (3D) generalized incompressible Navier-Stokes equations (gNS) in Triebel-Lizorkin space $\dot{F}^{-\alpha,r}_{q_\alpha}(\mathbb{R}^3)$ with…
We consider the derivative nonlinear Schr\"odinger equation on the real line, with a background function $\psi(t,x)\in L^\infty(\mathbb{R}^2)$ that satisfies suitable conditions. Such a function may, for example, be a non-decaying solution…
In this paper, we investigate a class of planar Schr\"{o}dinger-Poisson systems with critical exponential growth. We establish conditions for the local well-posedness of the Cauchy problem in the energy space, which seems innovative as it…
A global solvability result of the Cauchy problem of the two-species Vlasov-Maxwell-Landau system near a given global Maxwellian is established by employing an approach different than that of [5]. Compared with that of [5], the minimal…
In this work we shall show that the Cauchy problem \begin{equation} \left\{ \begin{aligned} &(u_t+u^pu_x+\mathcal H\partial_x^2u+ \alpha\mathcal H\partial_y^2u )_x - \gamma u_{yy}=0 \quad p\in{\nat} &u(0;x,y)=\phi{(x,y)} \end{aligned}…
In this article, we initiate the study of the Cauchy problem for the two-dimensional relativistic Euler equations in a low-regularity setting. By introducing good variables--a rescaled velocity, logarithmic enthalpy, and an appropriately…
In this paper, we study the well-posedness in critical Besov spaces for two-fluid Euler-Maxwell equations, which is different from the one fluid case. We need to deal with the difficulties mainly caused by the nonlinear coupling and…
In this article, we study the low-regularity Cauchy problem of a one dimensional quadratic Schrodinger system with coupled parameter $\alpha\in (0, 1)$. When $\frac{1}{2}<\alpha<1$,we prove the global well-posedness in $H^s(\mathbb{R})$…
In this paper, we study the Cauchy problem for the Benjamin-Ono-Burgers equation $\partial_t u-\epsilon \partial_x^2 u+\mathcal{H}\partial_x^2u+u u_x=0$, where $\mathcal{H}$ denotes the Hilbert transform. We obtain that it is uniformly…
In a fractional Sobolev space $H^s(\mathbb{R}^2)$ with $s\leq\frac74$, we prove the low-regularity ill-posedness for the 2D compressible Euler equations and the 2D ideal compressible MHD system. Our ill-posedness results match the…
We study the Cauchy problem for a quasilinear wave equation with low-regularity data. A space-time $L^2$ estimate for the variable coefficient wave equation plays a central role for this purpose. Assuming radial symmetry, we establish the…
The aim of this paper is to study the global existence of solutions to a coupled wave-Klein-Gordon system in space dimension two when initial data are small, smooth and mildly decaying at infinity. Some physical models strictly related to…
In this paper, we investigate the global well-posedness and optimal time-decay of classical solutions for the 3-D full compressible Navier-Stokes system, which is given by the motion of the compressible viscous and heat-conductive gases.…
This note is devoted to the study of the well-posedness of the Cauchy problem for the Landau Hamiltonian wave equation in the plane, with nonzero constant magnetic field. We show the well-posedness in suitably defined Sobolev spaces taking…
We prove global well-posedness and scattering for the massive Dirac-Klein-Gordon system with small and low regularity initial data in dimension two. To achieve this, we impose a non-resonance condition on the masses.
We extend recent results of S. Machihara and H. Pecher on low regularity well-posedness of the Dirac-Klein-Gordon (DKG) system in one dimension. Our proof, like that of Pecher, relies on the null structure of DKG, recently completed by…
We study global existence of solutions to the Cauchy problem for the wave equation with time-dependent damping and a power nonlinearity in the overdamping case. We prove the global well-posedness for small data in the energy space for the…