Global well-posedness of some high-order focusing semilinear evolution equations with exponential nonlinearity

Abstract

In even space dimensions, the initial value problems for some high-order focusing semilinear evolution equations with exponential nonlinearities are considered. Using the potential well method, global and nonglobal well-posedness in the energy space are obtained.

Keywords

• high-order wave type equation
• high-order schrödinger type equation
• high-order heat type equation
• ground state
• moser–trudinger inequality
• well-posedness
• blow-up
• 35q55
• 35b30