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In this paper, we prove the global existence of the weak solution to the mean field kinetic equation derived from the $N$-particle Newtonian system. For $L^1\cap L^\infty$ initial data, the… Click to show full abstract
In this paper, we prove the global existence of the weak solution to the mean field kinetic equation derived from the $N$-particle Newtonian system. For $L^1\cap L^\infty$ initial data, the solvability of the mean field kinetic equation can be obtained by using uniform estimates and compactness arguments while the difficulties arising from the non-local non-linear interaction are tackled appropriately using the Aubin-Lions compact embedding theorem.
Keywords:
kinetic equation;
mean field;
particle;
field kinetic
Journal Title: Mathematical Methods in the Applied Sciences
Year Published: 2019
Link to full text (if available)
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Journal Title: Mathematical Methods in the Applied Sciences
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!