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• W2036112329 abstract "We consider the Cauchy problem for the semilinear Schrödinger equation(NLS){(i∂t+Δ)u=μ|u|p,(t,x)∈[0,Tλ)×Rd,u(0,x)=λf(x),x∈Rd, where u=u(t,x) is a C-valued unknown function, μ∈C{0}, p>1, λ≥0, f=f(x) is a C-valued given function and Tλ is a maximal existence time of the solution. Our first aim in the present paper is to prove a large data blow-up result for (NLS) in Hs-critical or Hs-subcritical case p≤ps:=1+4/(d−2s), for some s≥0. More precisely, we show that in the case 1<p≤ps, for a suitable Hs-function f, there exists λ0>0 such that for any λ>λ0, the following estimatesTλ≤Cλ−κand{limt→Tλ−0⁡‖u(t)‖Hs=∞(if1<p<ps),‖u‖Ltr(0,Tλ;Bρ,2s)=∞(ifp=ps), hold, where κ,C>0 are constants independent of λ and (r,ρ) is an admissible pair (see Theorem 2.3). Our second aim is to prove non-existence local weak-solution for (NLS) in the Hs-supercritical case p>ps, which means that if p>ps, then there exists an Hs-function f such that if there exist T>0 and a weak-solution u to (NLS) on [0,T), then λ=0 (see Theorem 2.5)." @default.
• W2036112329 created "2016-06-24" @default.
• W2036112329 creator A5026324990 @default.
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• W2036112329 date "2015-05-01" @default.
• W2036112329 modified "2023-10-03" @default.
• W2036112329 title "Some non-existence results for the semilinear Schrödinger equation without gauge invariance" @default.
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• W2036112329 doi "https://doi.org/10.1016/j.jmaa.2015.01.003" @default.
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