ﻻ يوجد ملخص باللغة العربية
We construct solutions in $mathbb{R}^2$ with finite energy of the surface quasi-geostrophic equations (SQG) that initially are in $C^k$ ($kgeq 2$) but that are not in $C^{k}$ for $t>0$. We prove a similar result also for $H^{s}$ in the range $sin(frac32,2)$. Moreover, we prove strong ill-posedness in the critical space $H^{2}$.
This paper studies the dissipative generalized surface quasi-geostrophic equations in a supercritical regime where the order of the dissipation is small relative to order of the velocity, and the velocities are less regular than the advected scalar b
In this paper, we first establish the local well-posedness (existence, uniqueness and continuous dependence) for the Fornberg-Whitham equation in both supercritical Besov spaces $B^s_{p,r}, s>1+frac{1}{p}, 1leq p,rleq+infty$ and critical Besov spaces
Motivated by the paper by D. Gerard-Varet and E. Dormy [JAMS, 2010] about the linear ill-posedness for the Prandtl equations around a shear flow with exponential decay in normal variable, and the recent study of well-posedness on the Prandtl equation
In the paper, by constructing a initial data $u_{0}in B^{sigma}_{p,infty}$ with $sigma-2>max{1+frac 1 p, frac 3 2}$, we prove that the corresponding solution to the higher dimensional Camassa-Holm equations starting from $u_{0}$ is discontinuous at $
We prove that the Cauchy problem for the dispersion generalized Benjamin-Ono equation [partial_t u+|partial_x|^{1+alpha}partial_x u+uu_x=0, u(x,0)=u_0(x),] is locally well-posed in the Sobolev spaces $H^s$ for $s>1-alpha$ if $0leq alpha leq 1$. The n