报告题目：Global Regularity of weak solutions to the generalized Leray equations
报 告 人：郑孝信 博士
工作单位： 北京航空航天大学
报告时间：2021-07-01 15:00-16:00
腾讯会议ID： 568 307 423
入会访问链接： https://meeting.tencent.com/s/VReX4n1tkgqW
报告摘要：
We investigate a regularity for weak solutions of the following generalized Leray equations which arises from the study of self-similar solutions to the generalized Naiver-Stokes equations in R^3. Firstly, by making use of the vanishing viscosity and developing non-local effects of the fractional diffusion operator, we prove uniform estimates for weak solutions V in the weighted Hilbert space H^\alpha_{\omega}(R^3). Via the differences characterization of Besov spaces and the bootstrap argument, we improve the regularity for weak solution from H^\alpha_{\omega}(\R^3) to H_{\omega}^{1+\alpha}(\R^3). This regularity result, together linear theory for the non-local Stokes system, lead to pointwise estimates of V which allow us to obtain a natural pointwise property of the self-similar solution constructed in our recent work. In particular, we obtain an optimal decay estimate of the self-similar solution to the classical Naiver-Stokes equations by means of the special structure of Oseen tensor. This answers the question proposed by Tsai. This is a joint work with Lai Baishun and Miao Changxing.
报告人简介：
郑孝信，任职于北京航空航天大学数学科学学院，博士毕业于中国工程物理研究院，波兰Wroclaw University大学博士后。研究兴趣是Navier-Stokes，SQG，Boussinesq等流体力学方程。主持了2项国家自然科学基金项目， 在《Adv. Math.》、《Arch. Ration. Mech. Anal.》、《Comm. Math. Phys.》、《J. Math. Pures Appl.》、《SIAM J. Math. Anal.》、《J. Differential Equations》等著名期刊上发表SCI论文20余篇。
报告人简介：
郑孝信，任职于北京航空航天大学数学科学学院，博士毕业于中国工程物理研究院，波兰Wroclaw University大学博士后。研究兴趣是Navier-Stokes，SQG，Boussinesq等流体力学方程。主持了2项国家自然科学基金项目， 在《Adv. Math.》、《Arch. Ration. Mech. Anal.》、《Comm. Math. Phys.》、《J. Math. Pures Appl.》、《SIAM J. Math. Anal.》、《J. Differential Equations》等著名期刊上发表SCI论文20余篇。
郑孝信，任职于北京航空航天大学数学科学学院，博士毕业于中国工程物理研究院，波兰Wroclaw University大学博士后。研究兴趣是Navier-Stokes，SQG，Boussinesq等流体力学方程。主持了2项国家自然科学基金项目， 在《Adv. Math.》、《Arch. Ration. Mech. Anal.》、《Comm. Math. Phys.》、《J. Math. Pures Appl.》、《SIAM J. Math. Anal.》、《J. Differential Equations》等著名期刊上发表SCI论文20余篇。北京航空航天大学郑孝信博士网络学术报告
报告题目：Global Regularity of weak solutions to the generalized Leray equations
报 告 人：郑孝信 博士
工作单位： 北京航空航天大学
报告时间：2021-07-01 10:00-11:00
腾讯会议ID： 568 307 423
入会访问链接： https://meeting.tencent.com/s/VReX4n1tkgqW
报告摘要：
We investigate a regularity for weak solutions of the following generalized Leray equations which arises from the study of self-similar solutions to the generalized Naiver-Stokes equations in R^3. Firstly, by making use of the vanishing viscosity and developing non-local effects of the fractional diffusion operator, we prove uniform estimates for weak solutions V in the weighted Hilbert space H^\alpha_{\omega}(R^3). Via the differences characterization of Besov spaces and the bootstrap argument, we improve the regularity for weak solution from H^\alpha_{\omega}(\R^3) to H_{\omega}^{1+\alpha}(\R^3). This regularity result, together linear theory for the non-local Stokes system, lead to pointwise estimates of V which allow us to obtain a natural pointwise property of the self-similar solution constructed in our recent work. In particular, we obtain an optimal decay estimate of the self-similar solution to the classical Naiver-Stokes equations by means of the special structure of Oseen tensor. This answers the question proposed by Tsai. This is a joint work with Lai Baishun and Miao Changxing.
报告人简介：
郑孝信，任职于北京航空航天大学数学科学学院，博士毕业于中国工程物理研究院，波兰Wroclaw University大学博士后。研究兴趣是Navier-Stokes，SQG，Boussinesq等流体力学方程。主持了2项国家自然科学基金项目， 在《Adv. Math.》、《Arch. Ration. Mech. Anal.》、《Comm. Math. Phys.》、《J. Math. Pures Appl.》、《SIAM J. Math. Anal.》、《J. Differential Equations》等著名期刊上发表SCI论文20余篇。
