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Boling Guo

Publications and source records attributed to Boling Guo.

At least 37 records · Page 2Linked to original sources
arXiv2019

Global existence of the solution to Einstein-Yang-Mills-Higgs equations with small initial datum

The problem involved in this paper is the global existence of the solution to the $\mathfrak{su}(2)$-Einstein-Yang-Mills-Higgs(EYMH) equation. The approach we employ stems from H. Lindblad and I. Rodnianski and is dependent of wave coordinates and Lorentzian gauge conditions. Our main conclusion is that the EYMH system admits global existence provided the initial datum are sufficiently small. To the best of our knowledge, there is no similar result in the area of EYMH equations.

math-ph↗
arXiv2019

Existence and stability of periodic solution to the 3D Ginzburg-Landau equation in weighted Sobolev spaces

We prove the existence of time periodic solution to the 3D Ginzburg-Landau equation in weighted Sobolev spaces. We consider the cubic Ginzburg-Landau equation with an external force $g$ satisfying the oddness condition $g(-x,t)=-g(x,t)$. The existence of the periodic solution is proved for small time-periodic external force. The stability of the time periodic solution is also considered.

math.AP↗
arXiv2019

Navier-Stokes equations with external forces in Besov-Morrey spaces

We establish the existence and uniqueness of local strong solutions to the Navier-Stokes equations with arbitrary initial data and external forces in the homogeneous Besov-Morrey space. The local solutions can be extended globally in time provided the initial data and external forces are small. We adapt the method introduced in \cite{ks6}, where the Besov space is considered, to the setting of the homogeneous Besov-Morrey space.

math.AP↗
arXiv2019

Uniform local well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation

In this paper, we study the Cauchy problem for the Benjamin-Ono-Burgers equation $\partial_t u-ε\partial_x^2 u+\mathcal{H}\partial_x^2u+u u_x=0$, where $\mathcal{H}$ denotes the Hilbert transform. We obtain that it is uniformly locally well-posed for small data in the refined Sobolev space $\widetilde{H}^σ(\mathbb{R})$($σ\geq 0$), whose low-frequency part is scaling critical and high-frequency part is equal to Sobolev space $H^σ$($σ\geq 0$). Furthermore, we also obtain its inviscid limit behavior in $\widetilde{H}^σ(\mathbb{R})$($σ\geq 0$).

math.AP↗
arXiv2018

The Gerdjikov-Ivanov type derivative nonlinear Schrödinger equation: Long-time dynamics of nonzero boundary conditions

We consider the Gerdjikov--Ivanov type derivative nonlinear Schrödinger equation \berr \ii q_{t}+q_{xx}-\ii q^2\bar{q}_{x}+\frac{1}{2}(|q|^4-q_0^4)q=0 \eerr on the line. The initial value $q(x,0)$ is given and satisfies the symmetric, nonzero boundary conditions at infinity, that is, $q(x,0)\rightarrow q_\pm$ as $x\rightarrow\pm\infty$, and $|q_\pm|=q_0>0$. The goal of this paper is to study the asymptotic behavior of the solution of this initial-value problem as $t\rightarrow\infty$. The main tool is the asymptotic analysis of an associated matrix Riemann--Hilbert problem by using the steepest descent method and the so-called $g$-function mechanism. We show that the solution $q(x,t)$ of this initial value problem has a different asymptotic behavior in different regions of the $xt$-plane. In the regions $x<-2\sqrt{2}q_0^2t$ and $x>2\sqrt{2}q_0^2t$, the solution takes the form of a plane wave. In the region $-2\sqrt{2}q_0^2t<x<2\sqrt{2}q_0^2t$, the solution takes the form of a modulated elliptic wave.

math.AP↗
arXiv2018

Local Well and Ill Posedness for the Modified KdV Equations in Subcritical Modulation Spaces

We consider the Cauchy problem of the modified KdV equation (mKdV). Local well-posedness of this problem is obtained in modulation spaces $M^{1/4}_{2,q}(\mathbb{R})$ $(2\leq q\leq\infty)$. Moreover, we show that the data-to-solution map fails to be $C^3$ continuous in $M^{s}_{2,q}(\mathbb{R})$ when $s<1/4$. It is well-known that $H^{1/4}$ is a critical Sobolev space of mKdV so that it is well-posedness in $H^s$ for $s\geq 1/4$ and ill-posed (in the sense of uniform continuity) in $H^{s'}$ with $s'<1/4$. Noticing that $M^{1/4}_{2,q} \subset B^{1/q-1/4}_{2,q}$ is a sharp embedding and $H^{-1/4}\subset B^{-1/4}_{2,\infty}$, our results contains all of the subcritical data in $M^{1/4}_{2,q}$, which contains a class of functions in $H^{-1/4}\setminus H^{1/4}$.

math.AP↗
arXiv2018

Decay rates for the Viscous Incompressible MHD with and without Surface Tension

In this paper, we consider a layer of a viscous incompressible electrically conducting fluid interacting with the magnetic filed in a horizontally periodic setting. The upper boundary bounded by a free boundary and below bounded by a flat rigid interface. We prove the global well-posedness of the problem for both the case with and without surface tension. Moreover, we show that the global solution decays to the equilibrium exponentially in the case with surface tension, however the global solution decays to the equilibrium at an almost exponential rate in the case without surface tension.

math.AP↗
arXiv2018

Landau-Lifshitz-Bloch equation on Riemannian manifold

In this article, we bring in Landau-Lifshitz-Bloch(LLB) equation on $m$-dimensional closed Riemannian manifold and prove that it admits a unique local solution. In addition, if $m\geqslant3$ and $L^{\infty}-$norm of initial data is sufficiently small, the solution can be extended globally. Moreover, if $m=2$, we can prove that the unique solution is global without assuming small initial data.

math.AP↗
arXiv2018

Long-time asymptotics for the Hirota equation on the half-line

We consider the Hirota equation on the quarter plane with the initial and boundary values belonging to the Schwartz space. The goal of this paper is to study the long-time behavior of the solution of this initial-boundary value problem based on the asymptotic analysis of an associated matrix Riemann--Hilbert problem.

math.AP↗
arXiv2018

On the propagation of regularity and decay of solutions to the Benjamin equation

In this paper, we investigate some special regularities and decay properties of solutions to the initial value problem(IVP) of the Benjamin equation. The main result shows that: for initial datum $u_{0}\in H^{s}(\mathbb{R})$ with $s>3/4,$ if the restriction of $u_{0}$ belongs to $H^{l}((x_{0}, \infty))$ for some $l\in \mathbb{Z}^{+}$ and $x_{0}\in \mathbb{R},$ then the restriction of the corresponding solution $u(\cdot, t)$ belongs to $H^{l}((α, \infty))$ for any $α\in \mathbb{R}$ and any $t\in(0, T)$. Consequently, this type of regularity travels with infinite speed to its left as time evolves.

math.AP↗
arXiv2017

Initial-boundary value problem and long-time asymptotics for the Kundu--Eckhaus equation on the half-line

The initial-boundary value problem for the Kundu--Eckhaus equation on the half-line is considered in this paper by using the Fokas method. We will show that the solution $u(x,t)$ can be expressed in terms of the solution of a matrix Riemann--Hilbert problem formulated in the complex $k$-plane. Furthermore, based on a nonlinear steepest descent analysis of the associated Riemann--Hilbert problem, we can give the precise asymptotic formulas for the solution of the Kundu--Eckhaus equation on the half-line.

math.AP↗
arXiv2017

On the dynamics of Navier-Stokes-Fourier equations

In this paper we are concerned with a non-isothermal compressible Navier-Stokes-Fourier model with density dependent viscosity that vanish on the vacuum. We prove the global existence of weak solutions with large data in the three-dimensional torus $Ω=T^{3}$. The main point is that the pressure is given by $P=Rρθ$ without additional cold pressure assumption.

math.AP↗
arXiv2017

Local-in-time Well-posedness of Boundary Layer System for the Full Incompressible MHD Equations by Energy Methods

In this paper, we investigate the well-posedness theory for the MHD boundary layer system in two-dimensional space. The boundary layer equations are governed by the Prandtl type equations that are derived from the full incompressible MHD system with non-slip boundary condition on the velocity, perfectly conducting condition on the magnetic field, and Dirichlet boundary condition on the temperature when the viscosity coefficient depends on the temperature. To derive the Prandtl type boundary layer system, we require all the hydrodynamic Reynolds numbers, magnetic Reynolds numbers and Nusselt numbers tend to infinity at the same rate. Under the assumption that the initial tangential magnetic field is not zero, one applies the energy methods to establish the local-in-time existence and uniqueness of solution for the MHD boundary layer equations without the necessity of monotonicity condition.

math.AP↗
arXiv2016

Uniform Regularity and Vanishing Viscosity Limit for the Compressible Nematic Liquid Crystal Flows in Three Dimensional Bounded Domain

In this paper, we study the uniform regularity and vanishing viscosity limit for the compressible nematic liquid crystal flows in three dimensional bounded domain. It is shown that there exists a unique strong solution for the compressible nematic liquid crystal flows with boundary condition in a finite time interval which is independent of the viscosity coefficient. The solutions are uniform bounded in a conormal Sobolev space. Furthermore, we prove that the density and velocity are uniform bounded in $W^{1, \infty}$, and the director field is uniform bounded in $W^{3,\infty}$ respectively. Based on these uniform estimates, one also obtains the convergence rate of the viscous solutions to the inviscid ones with a rate of convergence.

math.AP↗
arXiv2016

On a nonisothermal ideal gas Navier-Stokes-Fourier equations

In this paper we are concerned with a non-isothermal compressible Navier-Stokes-Fourier model with density dependent viscosity that vanish on the vacuum. We prove sequential stability of variational weak solutions in periodic domain Ω= T3. The main point is that the pressure is given by P = Rρθ.

math.AP↗
arXiv2016

Global existence of weak solutions for generalized quantum MHD equation

We prove the existence of a weak solution to a generalized quantum MHD equation in a 2-dimensional periodic box for large initial data. The existence of a global weak solution is established through a three-level approximation, energy estimates, and weak convergence for the adiabatic exponent γ>1.

math.AP↗
arXiv2016

Uniform Regularity and Vanishing Viscosity Limit for the Nematic Liquid Crystal Flows in Three Dimensional Domain

In this paper, we investigate the uniform regularity and vanishing limit for the incompressible nematic liquid crystal flows in three dimensional bounded domain. It is shown that there exists a unique strong solution for the incompressible nematic liquid crystal flows with boundary condition in a finite time interval which is independent of the viscosity. The solution is uniformly bounded in a conormal Sobolev space. Finally, we also study the convergence rate of the viscous solutions to the inviscid ones.

math.AP↗