For nonnegative radially symmetric continuous initial data of mass 8π in the unit disk, the Jäger-Luckhaus system admits globally bounded classical solutions with the constant state 8 being globally exponentially asymptotically stable.
Ekvac.40(1997), no
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A note on the $8\pi$ problem of J\"ager-Luckhaus system
For nonnegative radially symmetric continuous initial data of mass 8π in the unit disk, the Jäger-Luckhaus system admits globally bounded classical solutions with the constant state 8 being globally exponentially asymptotically stable.