Global Behavior of Solutions to the Focusing Generalized Hartree Equation

We study behavior of solutions to the nonlinear generalized Hartree equation, where the nonlinearity is of nonlocal type and is expressed as a convolution iut+Δu+(|x|−(N−γ)∗|u|p)|u|p−2u=0,x∈RN,t∈R. Our main goal is to understand global behavior of solutions of this equation in various settings. In this work we make an initial attempt towards this goal and study H1 (finite energy) solutions. We first investigate the H1 local well-posedness and small data theory. We then, in the intercritical regime (0

Keywords:

• constant
• Mathematics
• Compact space
• Nonlinear system
• Hartree equation
• Mathematical analysis
• Interpolation inequality
• Convolution
• Uniqueness
• Small data

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