Abstract
We establish an almost optimal decay estimate for the 3-D Schrödinger equation with non-negative potential decaying exponentially and nonlinearity of power \( p > 1 + 2/3 = 5/3 \).The key point is the introduction of an appropriate analogue of the generators of the pseudoconformal group for the free Schrödinger equation.
Mathematics Subject Classification. Primary 35Q55, 35P10; Secondary 42B37, 42B35.
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Georgiev, V., Velichkov, B. (2012). Decay Estimates for the Supercritical 3-D Schrödinger Equation with Rapidly Decreasing Potential. In: Ruzhansky, M., Sugimoto, M., Wirth, J. (eds) Evolution Equations of Hyperbolic and Schrödinger Type. Progress in Mathematics, vol 301. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0454-7_8
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DOI: https://doi.org/10.1007/978-3-0348-0454-7_8
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