Zobrazeno 1 - 10
of 430
pro vyhledávání: '"Miao, Changxing"'
In this paper, we study the $L^p$ maximal estimates for the Weyl sums $\sum_{n=1}^{N}e^{2\pi i(nx + n^{k}t)}$ with higher-order $k\ge3$ on $\mathbb{T}$, and obtain the positive and negative results. Especially for the case $k=3$, our result is sharp
Externí odkaz:
http://arxiv.org/abs/2408.15527
Publikováno v:
Journal of Functional Analysis 287 (2024) 110527
In this paper, we investigate the Cauchy problem for the three dimensional inviscid Boussinesq system in the periodic setting. For $1\le p\le \infty$, we show that the threshold regularity exponent for $L^p$-norm conservation of temperature of this s
Externí odkaz:
http://arxiv.org/abs/2406.05337
Autor:
Chen, Xuezhi, Miao, Changxing
Let $\gamma(t)=(P_1(t),\ldots,P_n(t))$ where $P_i$ is a real polynomial with zero constant term for each $1\leq i\leq n$. We will show the existence of the configuration $\{x,x+\gamma(t)\}$ in sets of positive density $\epsilon$ in $[0,1]^n$ with a g
Externí odkaz:
http://arxiv.org/abs/2405.15400
We study $L^p$-boundedness of the Bochner-Riesz means for critical magnetic Schr\"odinger operators $\mathcal{L}_{\bf A}$ in ${\mathbb{R}^2}$, which involve the physcial Aharonov-Bohm potential. We show that for $1\leq p\leq +\infty$ and $p\neq 2$, t
Externí odkaz:
http://arxiv.org/abs/2405.02531
Fourier restriction conjecture is an important problem in harmonic analysis. Guo-Oh [17] studied the restriction estimates for quadratic surfaces of co-dimension 2 in $\mathbb{R}^5$. For one special surface $(\xi_1,\xi_2,\xi_3,\xi_1^2,\xi_2^2+\xi_1\x
Externí odkaz:
http://arxiv.org/abs/2404.09020
In this paper, we studied the space-time estimates for the solution to the Schr\"odinger equation. By polynomial partitioning, induction arguments, bilinear to linear arguments and broad norm estimates, we set up several maximal estimates for the Sch
Externí odkaz:
http://arxiv.org/abs/2402.13539
Local regularity for solutions to quasi-linear singular parabolic equations with anisotropic weights
Autor:
Miao, Changxing, Zhao, Zhiwen
This paper develops a concise procedure for the study on local behavior of solutions to anisotropically weighted quasi-linear singular parabolic equations of $p$-Laplacian type, which is realized by improving the energy inequalities and applying intr
Externí odkaz:
http://arxiv.org/abs/2312.02875
Autor:
Miao, Changxing, Zhao, Zhiwen
This paper aims to study the local behavior of solutions to a class of anisotropic weighted quasilinear degenerate parabolic equations with the weights comprising two power-type weights of different dimensions. We first capture the asymptotic behavio
Externí odkaz:
http://arxiv.org/abs/2310.20622
Autor:
Miao, Changxing, Zhao, Zhiwen
In this paper, a class of anisotropic weights having the form of $|x'|^{\theta_{1}}|x|^{\theta_{2}}|x_{n}|^{\theta_{3}}$ in dimensions $n\geq2$ is considered, where $x=(x',x_{n})$ and $x'=(x_{1},...,x_{n-1})$. We first find the optimal range of $(\th
Externí odkaz:
http://arxiv.org/abs/2310.01359
Publikováno v:
Bull. London Math. Soc., 55: 2705-2717 (2023)
In this paper, we show that for $\alpha\in(1/2,5/4)$, there exists a force $f$ and two distinct Leray-Hopf flows $u_1,u_2$ solving the forced fractional Navier-Stokes equation starting from rest. This shows that the J.L. Lions exponent is sharp in th
Externí odkaz:
http://arxiv.org/abs/2306.06358