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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Low regularity conservation laws for the fifth-order modified KdV equations in Besov spaces
Besov空间 五阶修正KdV方程 低正则性 守恒定律
2023/4/19
We get a priori estimates for the fifth-order modified KdV equations in Besov spaces with low regularity which cover the full subcritical range. These estimates are obtained from the power series expa...
The Harnack inequality for second-order parabolic equations with divergence-free drifts of low regularity
Harnack inequality second-order parabolic equations divergence-free drifts low regularity
2015/7/14
We establish the Harnack inequality for advection-diffusion equations with divergencefree drifts of low regularity.While our previous work [IKR] considered the elliptic case, here we treat the more ch...
Global well-posedness for the Kawahara equation with low regularity data
Kawahara equation global well-posedness Cauchy problem I-method
2012/3/1
We consider the global well-posedness for the Cauchy probelem of the Kawahara equation which is one of the fifth order KdV type equations. We first establish the local well-posedness in a more suitabl...
$L^q$ bounds on restrictions of spectral clusters to submanifolds for low regularity metrics
$L^q$ restrictions spectral clusters submanifolds low regularity metrics
2012/3/1
We prove $L^q$ bounds on the restriction of spectral clusters to submanifolds in Riemannian manifolds equipped with metrics of $C^{1,\alpha}$ regularity for $0 \leq \alpha \leq 1$. Our results allow f...
On the manifold structure of the set of unparameterized embeddings with low regularity
manifold structure unparameterized embeddings
2010/11/24
Given manifolds $M$ and $N$, with $M$ compact, we study the geometrical structure of the space of embeddings of $M$ into $N$, having less regularity than $\mathcal C^\infty$, quotiented by the group o...
We prove local existence and uniqueness of the Cauchy problem for a large class of tensorial second order linear hyperbolic partial differential equations with coefficients of low regularity in a suit...
Low regularity well-posedness for the 3D Klein-Gordon-Schrödinger system
the 3D Klein-Gordon-Schrö dinger system math
2010/11/19
The Klein-Gordon-Schr\"odinger system in 3D is shown to be locally well-posed for Schr\"odinger data in H^s and wave data in H^{\sigma} \times H^{\sigma -1}, if s > - \frac{1}{4}, \sigma > - \frac{1}...
On the equivariant implicit function theorem with low regularity and applications to geometric variational problems
equivariant implicit function theorem low regularity and applications variational problems
2010/12/14
We prove an implicit function theorem for functions on infinite dimensional Banach manifolds, invariant under the (local) action of a finite dimensional Lie group. Motivated by some geometric variatio...