On March 18, 2023, Andrei Gennad’evich Kulikovskii, an eminent contemporary scientist, an esteemed expert in continuum mechanics, and a full member of the Russian Academy of Sciences, celebrated his 90th birthday.

His scientific journey reflects a lifelong dedication to science, commencing during his studies at the Department of Hydromechanics of the Faculty of Mechanics and Mathematics of Moscow State University. Notably, Academician Leonid Ivanovich Sedov, a distinguished mechanician and the author of many fundamental results in this field, recognized Kulikovskii’s potential early on. This largely attests to the level of scientific abilities possessed by Kulikovskii, as earning the attention of a scientist of Sedov’s caliber was quite challenging. After completing his postgraduate studies at the Department of Hydromechanics in 1958 and defending his Ph.D. thesis, Kulikovskii joined the Department of Mechanics of the Steklov Mathematical Institute. At that time, the department was headed by Academician Sedov. Over the years, Kulikovskii achieved significant milestones: he defended his doctoral dissertation in 1969, became a corresponding member of the Russian Academy of Sciences in 1991, and attained in 2006 full membership of the academy within the Department of Energy, Mechanical Engineering, Mechanics and Control Processes. For a long time, Kulikovskii headed the Department of Mechanics at the Steklov Institute. Kulikovskii’s editorial prowess is evident in his tenure, from 2012 until recently, as the Editor-in-Chief of Fluid Dynamics, one of the most prestigious originally Russian journals in continuum mechanics. Moreover, Kulikovskii’s influence extends beyond leadership roles. He also published several monographs. His first monograph, Magnetohydrodynamics (co-authored by G. A. Lyubimov), remains a classic in the field. The latest of his published monographs, Mathematical Aspects of Numerical Solution of Hyperbolic Systems (co-authored by N. V. Pogorelov and A. Yu. Semenov), quickly became a bibliographic rarity.

L. I. Sedov possessed an exceptional talent for discerning prospective directions of research within the realm of continuum mechanics. The exploration of these directions promised significant advancements in the models of this field, which describe important fundamental and applied phenomena. One of such directions was magnetohydrodynamics (MHD), a science in its infancy at the time. It was under the astute observation of Sedov that the young Kulikovskii recognized the imperative to develop MHD. Subsequently, Kulikovskii solved a series of new important problems in this science and obtained a number of classical results. He was the first to study

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    nonlinear Riemann waves and the emergence of shock waves in the process of their overturning in MHD;

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    the problem of flow of a perfectly conducting fluid around bodies that have their own magnetic field; he constructed examples of such flows with the formation of a cavity—an area where the flow does not penetrate—near the body.

Together with G. A. Lyubimov, Kulikovskii authored a groundbreaking, world’s first monograph on magnetohydrodynamics. This book has become a seminal reference not only for students but also for seasoned experts in the field of the evolution of wave structures described by hyperbolic systems of equations.

Subsequently, Kulikovskii, together with his colleagues (G. A. Lyubimov and A. A. Barmin), studied ionization and recombination fronts; these are discontinuities in MHD on which additional boundary conditions obtained from the requirement for the existence of a discontinuity structure must hold. The number of these conditions depends on the velocity of the discontinuity. Kulikovskii showed that not only for the above-mentioned discontinuities, but also for an arbitrary discontinuity under very general conditions, the number of additional relations on the discontinuity obtained from the requirement for the existence of a structure ensures that the discontinuity is evolutionary. This is a fundamental result whose importance for the theory of hyperbolic waves is difficult to overestimate.

A. G. Kulikovskii also developed the theory of hyperbolic waves for other areas of continuum mechanics, including the theory of elasticity. Together with E. I. Sveshnikova, he obtained a number of significant results in the field of nonlinear waves in weakly anisotropic elastic media described by hyperbolic systems of partial differential equations. Their joint monograph Nonlinear Waves in Elastic Media is devoted to these results. In addition to hyperbolic waves in elastic media, they studied solidification fronts such that the state before the discontinuity front corresponds to a medium without tangential stresses and the state behind the discontinuity front corresponds to an elastic medium. At such discontinuities, just as in the case of ionization and recombination fronts, additional relations are required, and the number of these relations depends on the velocity of propagation of discontinuities in accordance with the requirements for them to be evolutionary.

A. G. Kulikovskii continued his research in the field of solutions of nonlinear hyperbolic wave equations in collaboration with A. P. Chugainova. They studied discontinuities and nonuniqueness of solutions for the problem of decay of an arbitrary discontinuity (Riemann problem) in nonlinear elastic media. In the study of discontinuous solutions of hyperbolic equations, an important role is played by small-scale phenomena; taking them into account allows one to transform a discontinuous solution into a continuous one in a narrow region. In this case, a shock wave is said to have a structure. Mathematically, this means adding terms with higher derivatives to the hyperbolic equations. If one uses discontinuities with stationary structure to construct a solution to the Riemann problem, then the solution turns out to be nonunique. It was found that a unique solution can be distinguished if it is spectrally stable. This made it possible to formulate a condition for the uniqueness of a discontinuous solution by including the requirement for the stability of its structure in the concept of an admissible discontinuity (in this case, the structure itself need not be stationary).

In 2003, for the results obtained in the above-mentioned areas, A. G. Kulikovskii (together with his coauthors) was awarded the State Prize of the Russian Federation.

A. G. Kulikovskii also obtained fundamental results in the theory of stability of perturbations in extended regions. He showed that distant boundaries of a region can cause instability by either amplifying perturbations (boundary instability) or contributing to the formation of a self-sustaining closed chain of waves that grows in time (global instability). For these results Kulikovskii was awarded the Chaplygin Prize in 1967. These results have been further developed; in particular, criteria were established for instability and growth of perturbations on a stationary inhomogeneous slowly varying background.

Moreover, A. G. Kulikovskii obtained a number of fundamental results on the evolution of small perturbations on the surface of a homogeneous unstable tangential discontinuity in an ideal fluid (together with I. S. Shikina), on nonlinear waves in magnets (together with N. I. Gvozdovskaya), and on the development of perturbations on a weakly inhomogeneous background (together with N. T. Pashchenko).

Along with successful scientific research, A. G. Kulikovskii pays great attention to teaching: for many years he has been a professor at the Department of Hydromechanics of the Faculty of Mechanics and Mathematics of Lomonosov Moscow State University. Many of his students have defended their candidate and doctoral dissertations, subsequently becoming renowned scientists. The scientific seminar led by A. G. Kulikovskii (together with V. P. Karlikov, O. E. Melnik, and A. N. Osiptsov) is a preeminent scientific event on continuum mechanics in Russia; presenting a talk at it is very prestigious and is highly esteemed by all scientists.

While principled, and sometimes even strict, in matters of science, Kulikovskii is known for his gentle and kind-hearted demeanor in everyday life. He is always ready to help people around him. His outstanding personal qualities serve as an inspiration to his younger colleagues.

Andrei Gennad’evich Kulikovskii stands as one of the most prominent contemporary scientists in mechanics; his unique perspective and expert opinion carries decisive weight in nearly every area of continuum mechanics. We extend our sincere congratulations and wish him continued health, happiness, and success in his scientific endeavors!

Editorial Board