ON THE SIMULTANEOUS RECOVERY OF ENVIRONMENTAL FACTORS IN THE 3D CHEMOTAXIS-NAVIER-STOKES MODELS

The mesmerizing dance of microorganisms within their aqueous habitats is a testament to the underlying forces that govern their movements. Among the numerous orchestrations of microbial motility, chemotaxis stands out as a fundamental biological phenomenon. Chemotaxis, i.e., the directed movement of biological cells in response to chemical gradients, is a captivating journey through the microscopic realm that plays a pivotal role in the survival and adaptability of various organisms. In this paper, we delve into the intricacies of chemotaxis and seek to understand the environmental factors involved in chemotaxis, such as the gravitational potential and the oxygen carrying-capacity. In particular, we focus on the unique identifiability issue of the 3D one- and two-species chemotaxis-Navier-Stokes model via application of the high-order variation method. We ensure the positivity of the solutions at all times to ensure their physical meanings and attempt to recover the exterior impact factors involved in the system. Our result provides a fresh perspective that differs from the inverse problem to comprehend and simulate this remarkable biological phenomenon.