# Olga Ladyzhenskaya

**Olga Aleksandrovna Ladyzhenskaya** (Russian: Óльга Алекса́ндровна Лады́женская; 7 March 1922 – 12 January 2004) was a Russian mathematician who worked on partial differential equations, fluid dynamics, and the finite difference method for the Navier–Stokes equations. She received the Lomonosov Gold Medal in 2002. She is the author of more than two hundred scientific works, among which are six monographs.

Olga Ladyzhenskaya | |
---|---|

Born | Olga Aleksandrovna Ladyzhenskaya 7 March 1922 |

Died | 12 January 2004 81) | (aged

Nationality | Soviet–Russian |

Alma mater | Moscow University |

Known for | Fluid dynamics of the Navier–Stokes equations, Hilbert's nineteenth problem, partial differential equations |

Awards | Lomonosov Gold Medal (2002) |

Scientific career | |

Fields | Partial differential equations |

Institutions | Saint Petersburg University |

Doctoral advisor | Ivan Petrovsky Sergei Sobolev |

Notable students | Nina Uraltseva Ludvig Faddeev Vladimir Buslaev |

## Biography

Ladyzhenskaya was born and grew up in the small town of Kologriv, the daughter of a mathematics teacher who is credited with her early inspiration and love of mathematics. The artist Gennady Ladyzhensky was her grandfather's brother, also born in this town. In 1937 her father, Aleksandr Ivanovich Ladýzhenski, was arrested by the NKVD and executed as an "enemy of the people".

Ladyzhenskaya completed high school in 1939, unlike her older sisters who weren't permitted to do the same. She was not admitted to Leningrad State University due to her father's status. Ladyzhenskaya attended a pedagogical institute then, after the German invasion of June 1941, taught school in Kologriv. She was finally admitted to Moscow State University in 1943 and graduated in 1947.[1]

Finally admitted to Leningrad State University, she received her PhD there under Sergei Sobolev and Vladimir Smirnov in 1951 and began teaching in the physics department in Leningrad in 1950. She received a second doctorate from Moscow State University in 1953. In 1954, she joined the mathematical physics laboratory of the Steklov Institute and became its head in 1961.[1][2]

Ladyzhenskaya had a love of arts and storytelling, counting writer Aleksandr Solzhenitsyn and poet Anna Akhmatova as her friends. She was once a member of the city council, had philanthropic efforts, and repeatedly risked her personal safety and career to aid those oppressed by the Soviet regime. Ladyzhenskaya suffered from various eye problems in her later years, and relied on special pencils to do her work. Two days before a trip to Florida, she passed away in her sleep in Russia on January 12, 2004.[3]

## Mathematical accomplishments

She was known for her work on partial differential equations (especially Hilbert's nineteenth problem) and fluid dynamics.[4] She provided the first rigorous proofs of the convergence of a finite difference method for the Navier–Stokes equations.[5]

She analyzed the regularity of parabolic equations, with Vsevolod A. Solonnikov and her student Nina Ural’tseva, and the regularity of quasilinear elliptic equations.[6]

She wrote a student theses under Ivan Petrovsky[7] and was on the shortlist for potential recipients for the 1958 Fields Medal,[8] ultimately awarded to Klaus Roth and René Thom.

## Publications

- Ladyzhenskaya, O.A. (1969) [1963],
*The Mathematical Theory of Viscous Incompressible Flow*, Mathematics and Its Applications,**2**(Revised Second ed.), New York; London; Paris; Montreux; Tokyo; Melbourne: Gordon and Breach, pp. xviii+224, MR 0254401, Zbl 0184.52603. - Ladyženskaja, O.A.; Solonnikov, V.A.; Ural'ceva, N.N. (1968),
*Linear and quasi-linear equations of parabolic type*, Translations of Mathematical Monographs,**23**, Providence, RI: American Mathematical Society, pp. xi+648, ISBN 978-0821886533, MR 0241821, Zbl 0174.15403. - Ladyzhenskaya, Olga A.; Ural'tseva, Nina N. (1968),
*Linear and Quasilinear Elliptic Equations*, Mathematics in Science and Engineering,**46**, New York and London: Academic Press, pp. xviii+495, ISBN 978-0080955544, MR 0244627, Zbl 0164.13002. - Ladyzhenskaya, O.A. (1985),
*The Boundary Value Problems of Mathematical Physics*, Applied Mathematical Sciences,**49**, Berlin; Heidelberg; New York: Springer Verlag, pp. xxx+322, doi:10.1007/978-1-4757-4317-3, ISBN 978-0521399227, MR 0793735, Zbl 0588.35003 (Translated by Jack Lohwater). - Ladyzhenskaya, O.A. (1991),
*Attractors for Semigroups and Evolution Equations*, Lezioni Lincee, Cambridge: Cambridge University Press, pp. xi+73, doi:10.1017/CBO9780511569418, ISBN 978-0521399227, MR 1133627, Zbl 0755.47049

## Awards and recognitions

- P. L. Chebyshev Prize (with Nina Nikolayevna Ural'tseva ) (1966) for the work “Linear and quasilinear equations of elliptic type”
- USSR State Prize (1969)
- Member of Lincei National Academy in Rome (1989)
- Member of the Russian Academy of Sciences (1990)
- Kovalevskaya Prize (1992) for the series of works "Attractors for Semigroups and Evolution Equations"
- ICM Emmy Noether Lecture (1994)
- John von Neumann Lecture (1998)
- Order of Friendship (1999)
- Lomonosov Gold Medal (2002) for outstanding achievements in the field of the theory of partial differential equations and mathematical physics
- On 7 March 2019, the 97th anniversary of Ladyzhenskaya's birth, the search engine Google released a Google Doodle commemorating her.[9][10] The accompanying comment read, "Today’s Doodle celebrates Olga Ladyzhenskaya, a Russian mathematician who triumphed over personal tragedy and obstacles to become one of the most influential thinkers of her generation."[9]

## Notes

- "Ladyzhenskaya, Olga Alexandrovna".
*www.encyclopedia.com*. Retrieved 7 March 2019. - Pearce, Jeremy (25 January 2004). "Dr. Olga Ladyzhenskaya, 81, Mathematician".
*New York Times*. Retrieved 10 March 2019. - https://massivesci.com/articles/olga-aleksandrovna-ladyzhenskaya-russian-mathematician-our-science-hero/
- See reference Bolibruch, Osipov & Sinai 2006, and also the comment of Peter Lax in (Pearce 2004)
- See reference Ладыженская 1958
- https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/ladyzhenskaya-olga-alexandrovna
- See the biography by Riddle (2010) from the Biographies of Women Mathematicians, Agnes Scott College.
- Barany, Michael (2018). "The Fields Medal should return to its roots".
*Nature*.**553**(7688): 271–273. Bibcode:2018Natur.553..271B. doi:10.1038/d41586-018-00513-8. PMID 29345675. - "Olga Ladyzhenskaya's 97th Birthday". 7 March 2019. Retrieved 7 March 2019.
- "Google Doodle: Who was Russian mathematician Olga Ladyzhenskay?".
*Evening Standard*. 6 March 2019. Retrieved 7 March 2019.

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## References

- Bolibruch, A.A.; Osipov, Yu. S.; Sinai, Ya. G., eds. (2006),
*Mathematical Events of the Twentieth Century*, Berlin; Heidelberg; New York: Springer-Verlag, pp. viii+545, Bibcode:2006metc.book.....A, doi:10.1007/3-540-29462-7, ISBN 978-3540232353, MR 2179060, Zbl 1072.01002 - Friedlander, Susan; Keyfitz, Barbara (18–20 May 2006), "Olga Ladyzhenskaya and Olga Oleinik: Two Great Women Mathematicians of the 20th Century" (PDF), in Kuperberg, Krystyna (ed.),
*Women in Mathematics: The Legacy of Ladyzhenskaya and Oleinik*, Berkeley, CA: AWM and MSRI, retrieved 1 July 2009. Some recollections of the authors about Olga Ladyzhenskaya and Olga Oleinik. - Friedlander, Susan; Lax, Peter; Synge Morawetz, Cathleen; Nirenberg, Louis; Seregin, Gregory; Ural’tseva, Nina; Vishik, Mark (December 2004), "Olga Alexandrovna Ladyzhenskaya (1922–2004)" (PDF),
*Notices of the American Mathematical Society*,**51**(11): 1320–1331, MR 2105237, Zbl 1159.01335. - Gunzburger, Max; Seregin, Gregory; Ochkur, Vitaly; Shilkin, Timofey (24 April 2004), "Obituaries: Olga Ladyzhenskaya" (PDF),
*SIAM News*,**37**(3): 3 - Pearce, Jeremy (25 January 2004), "Dr. Olga Ladyzhenskaya, 81, Mathematician",
*The New York Times*, retrieved 9 January 2012 - Riddle, Larry, ed. (8 December 2010),
*Olga Alexandrovna Ladyzhenskaya*, retrieved 5 May 2011. A biography in the Biographies of Women Mathematicians, Agnes Scott College. - Struwe, Michael (2003), "Olga Ladyzhenskaya — a life-long devotion to mathematics", in Hildebrandt, Stefan; Karcher, Hermann (eds.),
*Geometric analysis and nonlinear partial differential equations*, Berlin: Springer Verlag, pp. 1–10, ISBN 978-3540440512, MR 2008328, Zbl 1290.35002. - Synge Morawetz, Cathleen (18–20 May 2006), "Early Memories of Olga Ladyzhenskaya and Olga Oleinik" (PDF), in Kuperberg, Krystyna (ed.),
*Women in Mathematics: The Legacy of Ladyzhenskaya and Oleinik*, Berkeley, CA: AWM and MSRI, retrieved 1 July 2009. Some recollections of the author about Olga Ladyzhenskaya and Olga Oleinik. - Titova, Irina (26 January 2004), "Russian mathematician Olga Ladyzhenskaya dies at 81",
*USA Today*, retrieved 9 January 2012 - Zajączkowski, Wojciech (September 2005), "Olga Alexandrovna Ladyzhenskaya (1922–2004)",
*Topological Methods in Nonlinear Analysis*,**26**(1 2005): 5–7, doi:10.12775/TMNA.2005.021, MR 2179347, Zbl 1082.01516, archived from the original on 23 July 2011, retrieved 9 January 2012 - Ладыженская, О. А. (1958). "Решение "в целом" краевой задачи для уравнений Навье – Стокса в случае двух пространственных переменных".
*Доклады Академии наук СССР*.**123**(3): 427–429. [Ladyzhensakya, O. A. (1958). "Solution in the large to the boundary-value problem for the Navier–Stokes equations in two space variables".*Soviet Physics Dokl*.**123**(3): 1128–1131. Bibcode:1960SPhD....4.1128L.]

## External links

Wikimedia Commons has media related to .Olga Ladyzhenskaya |

- Beirao da Veiga, H.; Seregin, G.; Solonnikov, V.; Uraltseva, N.; Valli, A., eds. (2004),
*Partial Differential Equations in Mathematical Physics (October 24–30, 2004)*, Trento: CIRM, retrieved 1 February 2012. The schedule of a workshop in honour of Olga A. Ladyzhenskaya. - Kuperberg, Krystyna, ed. (18–20 May 2006),
*Women in Mathematics: The Legacy of Ladyzhenskaya and Oleinik*, Berkeley, CA: AWM and MSRI, retrieved 1 July 2009. The proceedings of a workshop in honour of Olga Ladyzhenskaya and Olga Oleinik. - Olga Ladyzhenskaya at the Mathematics Genealogy Project.
- O'Connor, John J.; Robertson, Edmund F. (August 2005), "Olga Alexandrovna Ladyzhenskaya",
*MacTutor History of Mathematics archive*, University of St Andrews.. - Olga Ladyzhenskaya at PlanetMath.org.
- Saint Petersburg Mathematical Society (2006),
*Olga Aleksandrovna Ladyzhenskaya*, retrieved 5 June 2011. Memorial page at the Saint Petersburg Mathematical Pantheon.