Zobrazeno 1 - 10
of 41
pro vyhledávání: '"Miao, Qianyun"'
In this paper, we investigate a class of inviscid generalized surface quasi-geostrophic (SQG) equations on the half-plane with a rigid boundary. Compared to the Biot-Savart law in the vorticity form of the 2D Euler equation, the velocity formula here
Externí odkaz:
http://arxiv.org/abs/2410.19273
We investigate global solutions to the Euler-alignment system in $d$ dimensions with unidirectional flows and strongly singular communication protocols $\phi(x) = |x|^{-(d+\alpha)}$ for $\alpha \in (0,2)$. Our paper establishes global regularity resu
Externí odkaz:
http://arxiv.org/abs/2308.09609
Let $\Omega\subset R^n$ be a bounded convex domain with $n\ge2$. Suppose that $A$ is uniformly elliptic and belongs to $W^{1,n}$ when $n\ge 3$ or $W^{1,q}$ for some $q>2$ when $n=2$. For $1
Externí odkaz:
http://arxiv.org/abs/2207.06143
In this paper, we study the Cauchy problem of the compressible Euler system with strongly singular velocity alignment. We prove the existence and uniqueness of global solutions in critical Besov spaces to the considered system with small initial data
Externí odkaz:
http://arxiv.org/abs/2207.02429
The paper concerns with the global well-posedness issue of the 2D incompressible inhomogeneous Navier-Stokes (INS) equations with fractional dissipation and rough density. We first establish the $L^q_t(L^p)$-maximal regularity estimate for the genera
Externí odkaz:
http://arxiv.org/abs/2111.12235
In this paper we address the temperature patch problem of the 2D viscous Boussinesq system without heat diffusion term. The temperature satisfies the transport equation and the initial data of temperature is given in the form of non-constant patch, u
Externí odkaz:
http://arxiv.org/abs/2110.06442
We study one-dimensional Eulerian dynamics with nonlocal alignment interactions, featuring strong short-range alignment, and long-range misalignment. Compared with the well-studied Euler-alignment system, the presence of the misalignment brings diffe
Externí odkaz:
http://arxiv.org/abs/2004.03652
Autor:
Miao, Qianyun, Zheng, Jiqiang
Publikováno v:
Colloquium Mathematicum, 140(2015),31-58
In this paper, we study the scattering theory for the defocusing energy-critical Klein-Gordon equation with a cubic convolution $u_{tt}-\Delta u+u+(|x|^{-4}\ast|u|^2)u=0$ in the spatial dimension $d \geq 5$. We utilize the strategy in [S. Ibrahim, N.
Externí odkaz:
http://arxiv.org/abs/1908.06904
Suppose that $n\ge3$ and $H(p)\in C^0(\mathbb{R}^n)$ is a locally strongly convex and concave Hamiltonian. We obtain the everywhere differentiability of all absolute minimizers for $H$ in any domain of $\mathbb{R}^n$.
Comment: 21 pages
Comment: 21 pages
Externí odkaz:
http://arxiv.org/abs/1901.10174
Suppose that $H \in C^0 (\mathbb{R}^2)$ satisfies \begin{enumerate} \item[(H1)] $H$ is locally strongly convex and locally strongly concave in $\rr^2$, \item[(H2)] $H(0)=\min_{p\in\rr^2}H(p)=0$. \end{enumerate} Let $\Omega\subset \rr^2$ be any domain
Externí odkaz:
http://arxiv.org/abs/1901.09539