scholarly journals The nonlinear stochastic Schrödinger equation via stochastic Strichartz estimates

2018 ◽  
Vol 18 (3) ◽  
pp. 1085-1114 ◽  
Author(s):  
Fabian Hornung
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Strichartz Estimates ◽  
Stochastic Schrödinger Equation

scholarly journals COUNTEREXAMPLES TO STRICHARTZ ESTIMATES FOR THE MAGNETIC SCHRÖDINGER EQUATION

2011 ◽  
Vol 13 (02) ◽  
pp. 213-234 ◽  
Author(s):  
LUCA FANELLI ◽  
ANDONI GARCIA
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Space Dimension ◽  
Strichartz Estimates

In space dimension n ≥ 3, we consider the magnetic Schrödinger Hamiltonian H = -(∇ - iA(x))2and the corresponding Schrödinger equation [Formula: see text] We show some explicit examples of potentials A, with less than Coulomb decay, for which any solution of this equation cannot satisfy Strichartz estimates, in the whole range of Schrödinger admissibility.

SPHERICAL AVERAGED ENDPOINT STRICHARTZ ESTIMATES FOR THE TWO-DIMENSIONAL SCHRÖDINGER EQUATION WITH INVERSE SQUARE POTENTIAL

2010 ◽  
Vol 07 (03) ◽  
pp. 365-382 ◽  
Author(s):  
I-KUN CHEN
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Strichartz Estimate ◽  
Strichartz Estimates ◽  
Angular Variable ◽  
Two Dimensional ◽  
Radial Variable

We investigate the two-dimensional Schrödinger equation with repulsive inverse square potential, and we prove the following homogeneous endpoint Strichartz estimate: [Formula: see text] where [Formula: see text] is a norm that applies L2average on the angular variable, first, and then the supremum on the radial variable.

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