Japan has suffered from secular stagnation for over a decade. The economy has been stuck on neutral even at ultra low interest rates. Some argue that the US has a similar problem. Growth has remained low even at zero short term interest rates. Growth in the US economy prior to the financial crisis was stimulated by household leverage during the real estate boom. The leverage from household debt will not be repeated soon.
Paul Krugman, argues that the Eurozone is headed for secular stagnation for similar reasons. Demographics are part of his explanation. The growth rate of working age workers in the eurozone is now where Japan was when its economy went to sleep. There will be less need for capital investment to support the shrinking labor force. Moreover, growth in the eurozone, prior to the financial crisis, was stimulated by leverage. The leverage in the eurozone came from a huge capital flow to the PGIIS. That is not likely to repeated soon.
Leaders in the eurozone seem to be more worried about inflation than they are about secular stagnation. With interest rates close to zero, a little bit of inflation would be good economic growth. It would bring real interest rates lower.