Endpoint Strichartz estimates for the magnetic Schrödinger equation
Copyright policy )Endpoint Strichartz estimates for the magnetic Schrödinger equation
We prove Strichartz estimates for the Schroedinger equation with an electromagnetic potential, in dimension $n\geq3$. The decay and regularity assumptions on the potentials are almost critical, i.e., close to the Coulomb case. In addition, we require repulsivity and a non trapping condition, which are expressed as smallness of suitable components of the potentials. However, the potentials themselves can be large, and we avoid completely any a priori spectral assumption on the operator. The proof is based on smoothing estimates and new Sobolev embeddings for spaces associated to magnetic potentials.
11 pages
- University of Pisa Italy
- Sapienza University of Rome Italy
- University of the Basque Country Spain
- Roma Tre University Italy
Soliton equations, dispersive equations; schrödinger equation; strichartz estimates; magnetic potential; schrodinger equation, magnetic potential, FOS: Physical sciences, Schrödinger equation, Mathematical Physics (math-ph), 58J45, Strichartz estimates, 35L05, Mathematics - Analysis of PDEs, Dispersion theory, dispersion relations arising in quantum theory, dispersive equations, FOS: Mathematics, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, Magnetic potential, Dispersive equations, 35L05; 58J45, Analysis, Mathematical Physics, Selfadjoint operator theory in quantum theory, including spectral analysis, Analysis of PDEs (math.AP)
Soliton equations, dispersive equations; schrödinger equation; strichartz estimates; magnetic potential; schrodinger equation, magnetic potential, FOS: Physical sciences, Schrödinger equation, Mathematical Physics (math-ph), 58J45, Strichartz estimates, 35L05, Mathematics - Analysis of PDEs, Dispersion theory, dispersion relations arising in quantum theory, dispersive equations, FOS: Mathematics, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, Magnetic potential, Dispersive equations, 35L05; 58J45, Analysis, Mathematical Physics, Selfadjoint operator theory in quantum theory, including spectral analysis, Analysis of PDEs (math.AP)
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