Mathematics Problem Archive

Can the Lavrentiev phenomenon occur for elastostatics under growth conditions ensuring that all finite-energy deformations are continuous?...

Prove global existence and uniqueness for suitable initial-boundary-value problems in dynamic nonlinear elasticity....

Establish global regularity, or exhibit breakdown, for solutions of the Vlasov–Maxwell equations from appropriate smooth initial data....

Develop a global-in-time theory of the Cauchy problem for the one-dimensional Euler–Fourier system for initial data constrained only by finite energy ...

Develop a compensated-compactness calculus for symmetric matrices when compensated compactness yields only inequalities. As a first application, prove...

For compressible Navier–Stokes equations with constant viscosities near vacuum, does the unphysical one-dimensional consequence identified by Hoff and...

Does the compressible Euler system in odd spatial dimension admit a nontrivial smooth eternal solution having finite nonzero mass and energy?...

Prove existence of a regular reflection for compressible flow against a wedge without assuming that the flow is irrotational....

For incompressible Navier-Stokes on $\mathbb{T}^d$, $d=2,3$, is the system approximately controllable and/or controllable in finite-dimensional projec...