中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：黄建华 教授 (国防科技大学)
题 目：退化噪声驱动的随机流体类发展方程的渐近性质
时 间：2021.12.07（星期二）, 08:40-09:40
地 点：腾讯会议，会议号639 997 201
摘 要：在这个报告中,我们介绍由中等退化噪声驱动的随机分数阶Boussinesq方程的适定性,马氏半群的指数衰减估计,给出其不变测度的存在唯一性和指数稳定性,再介绍强退化噪声驱动的随机分数阶MHD方程的适定性和指数遍历性,以及中心极限定理和大数定律等统计性质,比较退化噪声的强弱对系统渐近性质的影响. 该报告内容是与郑言和彭旭辉等合作完成的.
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报告人：闫 威 教授 (河南师范大学)
题 目：The Cauchy problem for the generalized ZK equation
时 间：2021.12.07（星期二）, 09:40-10:40
地 点：腾讯会议，会议号639 997 201
摘 要： In this paper, we consider the two-dimensional generalized Z-K equation
By establishing some new Strchartz estiamtes, we establish some bilinear estimates and trilinear estimates as well as some multilinear estimates and improve some well-posedness results. We also investigate pointwise convergence and uniform convergence.
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报告人：王明 教授 (中国地质大学(武汉))
题 目：KdV方程的解析半径与吸引子分形维数
时 间：2021.12.07（星期二）, 10:40-11:40
地 点：腾讯会议，会议号639 997 201
摘 要：本报告将介绍我们最近关于KdV方程的两个结果。其一，通过定义Gevrey函数类中的高阶修正能量，建立几乎能量守恒律(即Gevrey类中的I-方法)，证明了具有解析初值的KdV方程当时间趋于无穷时新的解析半径下界；其二，通过发掘KdV方程整体吸引子在无穷远处的小性，证明解半流满足Chueshov-Lasiecka拟稳定估计，得到了L2(R)中整体吸引子的有限分形维数。
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报告人：陈秀卿 教授 (中山大学)
题 目：A Note on Aubin-Lions-Dubinskii Lemmas
时 间：2021.12.09（星期四）, 14:30-15:30
地 点：腾讯会议，会议号908 152 940
摘 要：Strong compactness results for families of functions in seminormed nonnegative cones in the spirit of the Aubin-Lions-Dubinskii lemma are proven, refining some recent results in the literature. The first theorem sharpens slightly a result of Dubinskii (1965) for seminormed cones. The second theorem applies to piecewise constant functions in time and sharpens slightly the results of Dreher and Juengel (2012) and Chen and Liu (2012). An application is given, which is useful in the study of porous-medium or fast-diffusion type equations.
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报告人：吴兴龙 教授 (武汉理工大学)
题 目：The global existence and decay estimates of solutions of the compressible Euler equations with source terms in $\mathbb{R}^d$
时 间：2021.12.09（星期四）, 15:30-16:30
地 点：腾讯会议，会议号908 152 940
摘 要：The global existence and decay estimates of solutions of the compressible Euler equations with source terms in $\mathbb{R}^d$. In this talk, we first establish the existence and uniqueness of global smooth solution provided the initial data is sufficiently small, which tells us that the damping terms can prevents the development of singularity in small amplitude. Next, under the additional smallness assumption, the large time behavior of solution is investigated, which extends and improves the results obtained by Sideris et al. in CPDE.
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