Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  develops a method to rigorously show the validity of continuum description for the deterministic dynamics of many interacting particles with random initial data.  consider a hard sphere flow where particles are removed after the first collision. A fixed number of particles is drawn randomly according to an initial density $f_0(u,v)$ depending on $d$-dimensional position $u$ and velocity $v$. In the Boltzmann--Grad scaling,  derive the validity of a Boltzmann equation without gain term for arbitrary long times, when  assume finiteness of moments up to order two and initial data that are $L^\infty$ in space.  characterize the many-particle flow by collision trees which encode possible collisions. The convergence of the many-particle dynamics to the Boltzmann dynamics is achieved via the convergence of associated probability measures on collision trees. These probability measures satisfy nonlinear Kolmogorov equations, which are shown to be ll-posed by semigroup methods.
['Karsten Matthies', 'Florian Theil']
I am writing a research paper on a idea A Semigroup Approach to the Justification of Kinetic Theory
[{"from": "human", "value": "I am writing a research paper on a idea A Semigroup Approach to the Justification of Kinetic Theory"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  develops a method to rigorously show the validity of continuum description for the deterministic dynamics of many interacting particles with random initial data.  consider a hard sphere flow where particles are removed after the first collision. A fixed number of particles is drawn randomly according to an initial density $f_0(u,v)$ depending on $d$-dimensional position $u$ and velocity $v$. In the Boltzmann--Grad scaling,  derive the validity of a Boltzmann equation without gain term for arbitrary long times, when  assume finiteness of moments up to order two and initial data that are $L^\\infty$ in space.  characterize the many-particle flow by collision trees which encode possible collisions. The convergence of the many-particle dynamics to the Boltzmann dynamics is achieved via the convergence of associated probability measures on collision trees. These probability measures satisfy nonlinear Kolmogorov equations, which are shown to be ll-posed by semigroup methods."}]