Convex integration solutions to the transport equation with full dimensional concentration
2020; Elsevier BV; Volume: 37; Issue: 5 Linguagem: Inglês
10.1016/j.anihpc.2020.03.002
ISSN1873-1430
AutoresStefano Modena, Gabriel Sattig,
Tópico(s)Numerical methods in inverse problems
ResumoWe construct infinitely many incompressible Sobolev vector fields $u \in C_t W^{1,\tilde p}_x$ on the periodic domain $\mathbb{T}^d$ for which uniqueness of solutions to the transport equation fails in the class of densities $\rho \in C_t L^p_x$, provided $1/p + 1/\tilde p > 1 + 1/d$. The same result applies to the transport-diffusion equation, if, in addition $p'<d$.
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