<p><strong>Abstract :</strong> BGK (Bhatnagar-Gross-Krook) model is a relaxation-type model of the Boltzmann equation, which is popularly used in place of the Boltzmann equation in physics and engineering. In this talk, we address the ill-posedness problem for the BGK model, in which the solution instantly escapes the initial solution space. For this, we propose two ill-posedness scenarios, namely, the homogeneous and the inhomogeneous ill-posedness mechanisms. In the former case, we find a class of spatially homogeneous solutions to the BGK model, where removing the small velocity part of the initial data triggers ill-posedness by increasing temperature. For the latter, we construct a spatially inhomogeneous solution to the BGK model such that the local temperature constructed from the solution has a polynomial growth in spatial variable. These ill-posedness properties for the BGK model pose a stark contrast with the Boltzmann equation<br />
for which the solution map is, at least for a finite time, stable in the corresponding solution spaces. This is a joint work with Donghyun Lee (POSTECH) and Sungbin Park (POSTECH)</p>
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