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- W2964175648 abstract "Let S be a minimal mass blow up solution of the critical generalized KdV equation as constructed in [25] . We prove both time and space sharp asymptotics for S close to the blow up time. Let Q be the unique ground state of (gKdV), satisfying Q ″ + Q 5 = Q . First, we show that there exist universal smooth profiles Q k ∈ S ( R ) (with Q 0 = Q ) and a constant c 0 ∈ R such that, fixing the blow up time at t = 0 and appropriate scaling and translation parameters, S satisfies, for any m ⩾ 0 , ∂ x m S ( t ) − ∑ k = 0 [ m / 2 ] 1 t 1 2 + m − 2 k Q k ( m − k ) ( ⋅ + 1 t t + c 0 ) → 0 in L 2 as t ↓ 0 . Second, we prove that, for 0 < t ≪ 1 , x ⩽ − 1 t − 1 , S ( t , x ) ∼ − 1 2 ‖ Q ‖ L 1 | x | − 3 / 2 , and related bounds for the derivatives of S ( t ) of any order. We also prove ∫ R S ( t , x ) d x = 0 ." @default.
- W2964175648 created "2019-07-30" @default.
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- W2964175648 date "2017-03-01" @default.
- W2964175648 modified "2023-09-26" @default.
- W2964175648 title "Sharp asymptotics for the minimal mass blow up solution of the critical gKdV equation" @default.
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- W2964175648 doi "https://doi.org/10.1016/j.bulsci.2017.01.001" @default.
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