My research is mainly concerned with the qualitative theory of partial differential equations coming from fluid mechanics. At this point my focus is on the two most profound models - Navier-Stokes-Fourier system and complete Euler system of equations. These describe the motion of viscous and inviscid fluids including the heat transfer, respectively. Even after literally hundreds of years of systematical study by some of the brightest minds of their time, the mathematical knowledge about these models and their isentropic simplifications is still rather limited、especially in the "natural" 3 dimensional setting. The gap between math, physics, modelling and numerics is opening every day as in mathematics one has to balance between the complexity of the model (its accuracy in application) and the abilities of state-of-art tools and ideas of mathematical analysis. In my research I strive to create mathematical tools that could narrow the gap a little.
キーワード：Navier-Stokes system, Euler system, measure-valued solutions, qualitative theory, boundary conditions
2015.06.

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