Bounded Solutions of Ideal MHD with Compact Support in Space-Time
Daniel Faraco, Sauli Lindberg, László Székelyhidi
Abstract
Abstract We show that in 3-dimensional ideal magnetohydrodynamics there exist infinitely many bounded solutions that are compactly supported in space-time and have non-trivial velocity and magnetic fields. The solutions violate conservation of total energy and cross helicity, but preserve magnetic helicity. For the 2-dimensional case we show that, in contrast, no nontrivial compactly supported solutions exist in the energy space.
Topics & Concepts
Bounded functionMagnetohydrodynamicsIdeal (ethics)MathematicsEnergy (signal processing)Complex systemConservation lawElectromagnetismPhysicsMathematical analysisTotal energyMagnetic fieldConservation of energyClassical mechanicsEnergy conservationMagnetic energyIdeal gasEnergy methodUniform boundednessWeak solutionNavier-Stokes equation solutionsCosmology and Gravitation TheoriesAdvanced Mathematical Physics Problems