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Publication

Global well-posedness for the Yang-Mills equation in 4+1 dimensions: Small energy

Joachim Krieger
2017
Journal Articles

Abstract

We consider the hyperbolic Yang-Mills equation on the Minkowski space $\reels^{4+1}$ . Our main result asserts that this problem is globally well-posed for all initial data whose energy is sufficiently small. This solves a longstanding open problem.

Official source

Joachim Krieger
2017
Journal Articles

Abstract

Official source

Related concepts (19)

Energy poverty

Energy poverty is lack of access to modern energy services. It refers to the situation of large numbers of people in developing countries and some people in developed countries whose well-being is negatively affected by very low consumption of energy, use of dirty or polluting fuels, and excessive time spent collecting fuel to meet basic needs. Today, 759 million people lack access to consistent electricity and 2.6 billion people use dangerous and inefficient cooking systems.

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Primary energy (PE) is the energy found in nature that has not been subjected to any human engineered conversion process. It encompasses energy contained in raw fuels and other forms of energy, including waste, received as input to a system. Primary energy can be non-renewable or renewable. Primary energy is used in energy statistics in the compilation of energy balances, as well as in the field of energetics. In energetics, a primary energy source (PES) refers to the energy forms required by the energy sector to generate the supply of energy carriers used by human society.

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An energy transition (or energy system transformation) is a significant structural change in an energy system regarding supply and consumption. Currently, a transition to sustainable energy (mostly renewable energy) is underway to limit climate change. It is also called renewable energy transition. The current transition is driven by a recognition that global greenhouse-gas emissions must be drastically reduced. This process involves phasing-down fossil fuels and re-developing whole systems to operate on low carbon electricity.

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