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.^[1] 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".^[1]

Ladyzhenskaya completed high school in 1939, unlike her older sisters who weren't permitted to do the same. She was not admitted to the Leningrad State University due to her father's status and attended a pedagogical institute. After the German invasion of June 1941, she taught school in Kologriv. She was eventually admitted to Moscow State University in 1943 and graduated in 1947.^[2]

She began teaching in the Physics department of the university in 1950 and defended her PhD there, in 1951, under Sergei Sobolev and Vladimir Smirnov. She received a second doctorate from the Moscow State University in 1953. In 1954, she joined the mathematical physics laboratory of the Steklov Institute and became its head in 1961.^[2][3]

Ladyzhenskaya had a love of arts and storytelling, counting writer Aleksandr Solzhenitsyn and poet Anna Akhmatova among her friends. Like Solzhenitsyn she was religious.^[4] She was once a member of the city council, and engaged in philanthropic activities, repeatedly risking her personal safety and career to aid people opposed to 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 died in her sleep in Russia on 12 January 2004.^[5]

Ladyzhenskaya is known for her work on partial differential equations (especially Hilbert's nineteenth problem) and fluid dynamics.^[6] She provided the first rigorous proofs of the convergence of a finite difference method for the Navier–Stokes equations.^[7]

She analyzed the regularity of parabolic equations, with Vsevolod A. Solonnikov and her student Nina Ural'tseva, and the regularity of quasilinear elliptic equations.^[2]

She wrote a student thesis under Ivan Petrovsky^[8] and was on the shortlist for the 1958 Fields Medal,^[9] ultimately awarded to Klaus Roth and René Thom.

• Ladyzhenskaya, O.A. (1969) [1963], The Mathematical Theory of Viscous Incompressible Flow, Mathematics and Its Applications, vol. 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, vol. 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, vol. 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, vol. 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, S2CID 51684720, Zbl 0755.47049

• 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.^[10][11] 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."^[10]
• In 2022, the "Ladyzhenskaya Prize in Mathematical Physics" is created in her honor. It has been awarded for the first time on 2 July 2022 to Svetlana Jitomirskaya in a joint session at (WM)², World Meeting for Women in Mathematics and at the Probability and Mathematical Physics conference OAL Prize Winner 2022.^[12]

• Projection method (fluid dynamics)

• 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", in Kuperberg, Krystyna (ed.), Women in Mathematics: The Legacy of Ladyzhenskaya and Oleinik, Berkeley, CA: AWM and MSRI, archived from the original (PDF) on 8 March 2018, 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, archived from the original (PDF) on 7 July 2014, retrieved 9 January 2012
• 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", in Kuperberg, Krystyna (ed.), Women in Mathematics: The Legacy of Ladyzhenskaya and Oleinik, Berkeley, CA: AWM and MSRI, archived from the original (PDF) on 8 March 2018, 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
• 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.]

• 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: Centro Internazionale per la Ricerca Matematica, 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, archived from the original on 8 March 2018, 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.
• Saint Petersburg Mathematical Society (2006), Olga Aleksandrovna Ladyzhenskaya, retrieved 5 June 2011. Memorial page at the Saint Petersburg Mathematical Pantheon.