arXiv subjects
Publications and source records attributed to Yanghai Yu.
In the paper, we consider the initial value problem to the higher dimensional Euler equations in the whole space. Based on the new technical which is developed in \cite{Li2}, we proved that the data-to-solution map of this problem is not uniformly continuous in nonhomogeneous Besov spaces in the sense of Hadamard. Our obtained result improves considerably the recent result given by Pastrana \cite{Pastrana}.
In the paper, we consider the initial value problem to the Camassa-Holm equation in the real-line case. Based on the local well-posedness result and the lifespan, we proved that the data-to-solution map of this problem is not uniformly continuous in nonhomogeneous Besov spaces in the sense of Hadamard. Our obtained result improves considerably the result in \cite{H-K}.
In this paper, we consider the Cauchy problem of the multi-dimensional generalized MHD system in the whole space and construct global smooth solutions with a class of large initial data by exploring the structure of the nonlinear term. Precisely speaking, our choice of special initial data whose $L^{\infty}$ norm can be arbitrarily large allows to generate global-in-time solutions to the generalized MHD system.
In this paper, we establish the global regularity for the 3D tropical climate model with fractional dissipation.
In this paper, we derive a new smallness hypothesis of initial data for the three-dimensional incompressible Navier-Stokes equations. That is, we prove that there exist two positive constants $c_0,C_0$ such that if \begin{equation*} \|u_0^1+u^2_0,u^3_0\|_{\dot{B}_{p,1}^{-1+\frac{3}{p}}} \|u^1_0,u^2_0\|_{\dot{B}_{p,1}^{-1+\frac{3}{p}}} \exp\{C_0 (\|u_0\|^{2}_{\dot{B}_{\infty,2}^{-1}}+\|u_0\|_{\dot{B}_{\infty,1}^{-1}})\} \leq c_0, \end{equation*} then \eqref{NS} has a unique global solution. As an application we construct two family of smooth solutions to the Navier-Stokes equations whose $\B^{-1}_{\infty,\infty}(\mathbb{R}^3)$ norm can be arbitrarily large.
In this paper, we construct a class of global large solution to the compressible Navier-Stokes equations in the whole space $\R^d$. Precisely speaking, our choice of special initial data whose $\dot{B}^{-1}_{\infty,\infty}$ norm can be arbitrarily large, namely, $||u_0||_{\dot{B}^{-1}_{\infty,\infty}}\gg 1$, allows to give rise to global-in-time solution to the compressible Navier-Stokes equations.
In this paper, we establish the global existence to the three-dimensional incompressible Hall-MHD equations for a class of large initial data, whose $L^{\infty}$ norms can be arbitrarily large.
In this paper, we construct a class global large solution to the two-dimensional MHD equations with damp terms in the nonhomogeneous Sobolev framework.
In this paper we consider the Cauchy problem to the Korteweg system with the general pressure in dimension $d\geq2$, and establish the global well-posedness of strong solution for the small initial data in $L^p$ type critical Besov spaces by using the Friedrich method and compactness arguments. Furthermore, we also obtain the optimal decay rate for the Korteweg system in $L^2$ type Besov spaces.
In this paper we consider the global well-posedness of compressible magnetohydrodynamic system in $\R^d$ with $d\geq2$, in the framework of the critical Besov spaces. We can show that if the initial data, the shear viscosity and the magnetic diffusion coefficient are small comparing with the volume viscosity, then compressible magnetohydrodynamic system has a unique global solution.