Anomalous Dissipation and the Strong Onsager Conjecture Part 1 (the local energy inequality) скачать в хорошем качестве

Anomalous Dissipation and the Strong Onsager Conjecture Part 1 (the local energy inequality)

Anomalous dissipation refers to the phenomenon of unusual or deviant energy losses in certain physical systems, particularly in turbulent flows. It describes the process by which energy from macroscopic motions is transferred to smaller scales and eventually dissipated in the form of heat or other forms of energy loss. The Strong Onsager Conjecture is a hypothesis postulated by Lars Onsager, a Norwegian physicist. It pertains to the mathematical description of dissipation in turbulent flow and posits that certain coefficients in the equations describing energy transfer between different scales of the flow should exhibit symmetry. Essentially, the Strong Onsager Conjecture states that the energy transfer between scales in turbulent flows should not depend on the direction. In other words, the mathematical equations describing the energy transfer should be valid for both the energy flow from larger to smaller scales and vice versa. The Strong Onsager Conjecture is an active area of research in the theory of turbulent flows and holds significant importance in understanding and modeling phenomena such as vortices, turbulence, and energy transfer in various physical systems. However, it has not yet received general mathematical confirmation or proof and continues to be the subject of intense investigation and discussion within the physics community.