[1]Bourgain J., Korobkov M. V., Kristensen J. (2015): On the Morse–Sard property and level sets of Wn,1 Sobolev functions on Rn,” Journal fur die reine und angewandte Mathematik (Crelles Journal), 2015, No. 700, 93–112. http://dx.doi.org/10.1515/crelle-2013-0002

[2]J. Bourgain, M.V. Korobkov and J. Kristensen (2013): On the Morse– Sard property and level sets of Sobolev and BV functions, Rev. Mat. Iberoam., 29, no. 1, 1–23. http://dx.doi.org/10.4171/rmi/710

[3]M.V. Korobkov, K. Pileckas and R. Russo (2015): Solution of Leray’s problem for stationary Navier-Stokes equations in plane and axially symmet- ric spatial domains, Annals of Math., 181, no. 2, 769-807. http://dx.doi.org/10.4007/annals.2015.181.2.7

[4]Korobkov M., Kristensen J. (2018): The Trace Theorem, the Luzin N – and Morse–Sard Properties for the Sharp Case of Sobolev–Lorentz Mappings, J. Geom. Anal., 28, no. 3, p.2834–2856, https://doi.org/10.1007/s12220-017-9936-7

[5]Korobkov M.V., Pileckas K., Russo R. (2018): The existence theorem for the steady Navier–Stokes problem in exterior axially symmetric 3D domains, Math. Ann., 370, no. 1–2, p.727–784. https://doi.org/10.1007/s00208-017-1555-x

[6]Ferone A., Korobkov M.V., Roviello A., (2019): On the Luzin N-property and the uncertainty principle for Sobolev mappings, Analysis and PDEs, 12, no. 5, p.1149–1175. http://doi.org/10.2140/apde.2019.12.1149

[7]M.V. Korobkov, K. Pileckas and R. Russo (2019): On convergence of arbitrary D-solution of steady Navier–Stokes system in 2D exterior domains, Arch. Rational Mech. Anal., 233, no. 1, p. 385–407 http://doi.org/10.1007/s00205-019-01359-8

[8]Hajlasz P., Korobkov M.V., Kristensen J. (2017): A bridge between Dubovitskii-Federer theorems and the coarea formula, J. Funct. Anal., 272, no. 3, p.1265–1295. http://dx.doi.org/10.1016/j.jfa.2016.10.031

[9]M. Korobkov and T.-P. Tsai (2016): Forward self-similar solutions of the Navier–Stokes equations in the half space, Analysis and PDE, 9, no. 8. p. 1811–1827. http://dx.doi.org/10.2140/apde.2016.9.1811

[10]Korobkov M.V., Pileckas K., Russo R. (2016): Leray’s Problem on Ex- istence of Steady State Solutions for the Navier-Stokes Flow, in Handbook of Mathematical Analysis in Mechanics, Springer International Publishing AG, Y. Giga, A. Novotny (eds.), P.1-50, dx.doi.org/10.1007/978-3319-10151-4 5-1

[11]M.V. Korobkov, K. Pileckas and R. Russo (2015): Steady Navier-Stokes system with nonhomogeneous boundary conditions in the axially symmetric case, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 14, No. 1 (2015), 233–262. http://dx.doi.org/10.2422/2036-2145.201204 003

[12]M. V. Korobkov and J. Kristensen (2014): On the Morse-Sard Theorem for the sharp case of Sobolev mappings, Indiana Univ. Math. J., 63, No. 6, 1703–1724. http://dx.doi.org/10.1512/iumj.2014.63.5431

[13]M.V. Korobkov, K. Pileckas and R. Russo (2014): The existence of a solution with finite Dirichlet integral for the steady Navier-Stokes equations in a plane exterior symmetric domain, J. Math. Pures. Appl. 101, no. 3, 257–274. http://dx.doi.org/10.1016/j.matpur.2013.06.002

[14]M.V. Korobkov, K. Pileckas, V. V. Pukhnachev, and R. Russo (2014): The flux problem for the Navier-Stokes equations, Russian Math. Surveys, 69, No. 6, 1065–1122. http://dx.doi.org/10.1070/RM2014v069n06ABEH004928

[15]M.V. Korobkov, K. Pileckas and R. Russo (2013): On the flux prob- lem in the theory of steady Navier–Stokes equations with nonhomogeneous boundary conditions, Arch. Rational Mech. Anal. 207, no. 1, 185–213. http://dx.doi.org/10.1007/s00205-012-0563-y.

[16]M.V. Korobkov, K. Pileckas and R. Russo (2012): Steady Navier-Stokes system with nonhomogeneous boundary conditions in the axially symmetric case, Comptes rendus – Mecanique 340, 115–119.

[17]Korobkov, M. V. (2011): Bernoulli law under minimal smoothness as- sumptions. Dokl. Math. 83, no.1, 107-110.

[18]Korobkov, M. V. (2010): Properties of C1-smooth functions whose gra- dient range has topological dimension 1. Dokl. Math. 81, no.1, 11-13.

[19]Korobkov, M. V. (2009): Properties of C1-smooth mappings with a one- dimensional gradient range. Sib. Math. J. 50, no. 5, 874-886.

[20]Korobkov, M. V. (2010): A criterion for the unique determination of domains in Euclidean spaces by the metric of the boundary induced by the intrinsic metric of the domain. Siberian Advances in Math. 20, no. 4, 256- 284.

[21]Korobkov, M. V. (2008): Necessary and sufficient conditions for the unique determination of plane domains. Sib. Math. J. 49, no. 3, 436-451.

[22]Korobkov, M. V. (2008): An example of a C1-smooth function whose gradient range is an arc with no tangent at any point. Sib. Math. J. 49, no. 1, 109-116.

[23]Korobkov, M. V. (2007): Necessary and sufficient conditions for the unique determination of plane domains. Dokl. Math. 76, no. 2, 722-723.

[24]Korobkov, M. V. (2007): Properties of C1-smooth functions with a nowhere dense gradient range. Siberian Math. J. 48, no. 6, 1019-1028.

[25]Korobkov, M. V.; Panov, E. Yu. (2007): Necessary and sufficient condi- tions for a curve to be the gradient range of a C1-smooth function. Siberian Math. J. 48, no. 4, 629-647.

[26]Korobkov, M. V. (2006): Properties of C1-smooth functions whose range of the gradient is a nowhere dense set. Dokl. Akad. Nauk 410, no. 5, 596- 598.

[27]Korobkov, M. V.; Panov, E. Yu. (2006): On necessary and sufficient conditions for a curve to be the range of the gradient of a C1-smooth function. Dokl. Akad. Nauk 410, no. 4, 449-452.

[28]Korobkov, M. V. (2006): On an analogue of Sard’s theorem for C1- smooth functions of two variables. Siberian Math. J. 47, no. 5, 889-895.

[29]Korobkov, M. V.; Panov, E. Yu. (2006): On isentropic solutions of first-order quasilinear equations. Sb. Math. 197, no. 5-6, 727-752.

[30]Kopylov, A. P.; Korobkov, M. V.; Ponomarev, S. P. (2003):  Stability in the Cauchy and Morera theorems for holomorphic functions and their three-dimensional analogues. Siberian Math. J. 44, no. 1, 99-108.

[31]Korobkov, M. V. (2002): Stability in the C-norm and in the W_∞¹-norm of classes of Lipschitz functions of one variable. Siberian Math. J. 43, no. 5, 827-842.

[32]Egorov, A. A.; Korobkov, M. V. (2001): On the stability of classes of affine mappings. Siberian Math. J. 42, no. 6, 1047-1061.

[33]Korobkov, M. V. (2001): On a generalization of the Lagrange and Dar- boux theorems to vector-valued functions. Dokl. Akad. Nauk 377, no. 5, 591-593.

[34]Korobkov, M. V. (2001): A generalization of Lagrange’s mean value theorem to the case of vector-valued mappings. Siberian Math. J. 42, no. 2, 297-300.

[35]Egorov, A. A.; Korobkov, M. V. (2000): Stability of classes of Lipschitz mappings, the Darboux theorem, and quasiconvex sets. Siberian Math. J. 41, no. 5, 855-865.

[36]Korobkov, M. V.; Egorov, A. A. (2000): Stability of classes of Lipschitz mappings, the Darboux theorem, and quasiconvex sets. Dokl. Akad. Nauk 373, no. 5, 583-587.

[37]Korobkov, M. V. (2000): On the stability of classes of Lipschitz mappings generated by compact sets of the space of linear mappings. Siberian Math. J. 41, no. 4, 656-670.

[38]Korobkov, M. V. (2000): On a generalization of Darboux’s theorem to the multidimensional case. Siberian Math. J. 41, no. 1, 100-112.

[39]Korobkov, M. V. (1998): On a generalization of the connectedness con- cept and its application to differential calculus and to the theory of stability of classes of mappings. Dokl. Akad. Nauk 363, no. 5, 590–593.

[40]Korobkov, M. V.; Panov, E. Yu. (2007): On the theory of isentropic solutions of quasilinear conservation laws. J. Math. Sci. (N. Y.) 144, no. 1, 3815–3824.

[41]Korobkov, M. (2003): On stability of a class of convex functions. In: Progress in analysis, Vol. I, II (Berlin, 2001), 207-213, World Sci. Publ., River Edge, NJ.

[42]Korobkov M.V., Pileckas K., Russo R. (2015): The Liouville Theorem for the Steady-State Navier–Stokes Problem for Axially Symmetric 3D Solutions in Absence of Swirl. J. Math. Fluid Mech., 17, p. 287–293. https://doi.org/10.1007/s00021-015-0202-0

[43]Korobkov M.V., Pileckas K., Russo R. (2020): Solvability in a finite pipe of steady-state Navier–Stokes equations with boundary conditions involving Bernoulli pressure. Calc. Var. 59, no. 32. https://doi.org/10.1007/s00526-019-1688-8

[44]Korobkov M.V., Pileckas K., Russo R. (2020): On the steady Navier- Stokes equations in 2D exterior domains. J. Differential Equations, 269, no. 3, P. 1796–1828. https://doi.org/10.1016/j.jde.2020.01.012

[45]Korobkov M.V., Pileckas K., Russo R. (2020): A Simple Proof of Reg- ularity of Steady-State Distributional Solutions to the Navier–Stokes Equa- tions. J. Math. Fluid Mech. 22, no.55, https://doi.org/10.1007/s00021-020-00517-3

[46]Korobkov M.V., Pileckas K., Russo R. (2020): Leray’s plane steady state solutions are nontrivial. Advances in Mathematics, https://doi.org/10.1016/j.aim.2020.107451

[47]Ferone A., Korobkov M.V., Roviello A., (2019): Morse–Sard theorem and the Luzin N-property: a new synthesis for smooth and Sobolev spaces, Siberian Mathematical J., 60, no. 5, 916–926. http://doi.org/10.1134/S0037446619050148

[48]Ferone A., Korobkov M.V., Roviello A., (2020): On some universal Morse–Sard type theorem, J. Math. Pures. Appl., 139, 1–34. https://doi.org/10.1016/j.matpur.2020.05.002

Seminar Title: Fudan International Seminar on Analysis PDEs and Fluid Mechanics

Dear Colleagues!

The new meeting of  “Fudan International Seminar on Analysis, PDEs, and Fluid

mechanics”  will take place on Thursday, November 26. 

The next  talk:

Xiao Ren (Fudan University)

Title of the talk: The uniqueness of Plane Stationary Navier-Stokes Flow Past an Obstacle

Time: Thursday, 26 of November, 21:00 -- 22:00 (Shanghai time), 14:00 -- 15:00 (Paris time), 8:00-- 9:00 a.m. (US ET)

Abstract: We study the exterior problem for stationary Navier-Stokes equations in two dimensions describing a viscous incompressible fluid flowing past an obstacle. It is shown that, at small Reynolds numbers, the classical solutions constructed by Finn and Smith are unique in the class of D-solutions (i.e., solutions with finite Dirichlet integral). No additional symmetry or decay assumptions are required. This result answers a long-standing open problem. The talk is based on a joint paper with M.Korobkov.

ZOOM link:

https://us02web.zoom.us/j/83673138944?pwd=azQyc1BwUjJFY3VjMStLbFR5Z2VwUT09

ZOOM Id: 836 7313 8944

Passcode: 808818

The more detailed information concerning schedule, etc., see on the seminar web page

https://researchseminars.org/seminar/Cafe_Analysis_and_Fluid

We sincerely hope you will be able to participate.

Best regards,

Organizing Committee: Professors Zhen Lei, Mikhail Korobkov, Adele Ferone, Remigio Russo, and Konstantin Pileckas

The seminar is organized by Fudan University (Shanghai, China) with the collaboration of Universita degli studi della Campania "Luigi Vanvitelli" (Caserta, Italy) and Vilnius University (Vilnius, Lithuania). This seminar is meant to gather renowned experts working on Geometric and Real Analysis with applications to PDEs and Mathematical Physics and represents an opportunity for presenting high-impact research, as well as facilitating the exchange of ideas between researchers. 

Lectures are scheduled for each Thursday, by ZOOM, with 60 minutes every talk.