Existence and Non-uniqueness of Global Weak Solutions to Inviscid Primitive and Boussinesq Equations

Abstract

We consider the initial value problem for the inviscid Primitive and Boussinesq equations in three spatial dimensions. We recast both systems as an abstract Eulertype system and apply the methods of convex integration of De Lellis and Székelyhidi to show the existence of infinitely many global weak solutions of the studied equations for general initial data. We also introduce an appropriate notion of dissipative solutions and show the existence of suitable initial data which generate infinitely many dissipative solutions.

On global-in-time weak solutions to the magnetohydrodynamic system of compressible inviscid fluids

“…This is the initial energy jump typical for weak solutions obtained through the method of convex integration; see [8,9,19]. Nevertheless, it is possible to remove this drawback by modifying the convex integration scheme as explained in [9,20], at least for certain initial velocity.…”

Bounded Solutions of Ideal MHD with Compact Support in Space-Time

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Exponential time differencing for the tracer equations appearing in primitive equation ocean models

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