24 citations · 164 across the 45 of their papers we have counts for
11 papers · 2 filters
Norm-inflation results for the BBM equation
Jerry Bona, Mimi Dai
Considered here is the periodic initial-value probem for the regularized long-wave (BBM) equation \[u_t+u_x+uu_x-u_{xxt}=0.\] Adding to previous work in the literature, it is shown…
Ill-posedness of the Navier-Stokes and magneto-hydrodynamics systems
Alexey Cheskidov, Mimi Dai
We demonstrate that the three dimensional incompressible magneto-hydrodynamics (MHD) system is ill-posed due to the discontinuity of weak solutions in a wide range of spaces. Speci…
Kolmogorov's dissipation number and the number of degrees of freedom for the 3D Navier-Stokes equations
Alexey Cheskidov, Mimi Dai
Kolmogorov's theory of turbulence predicts that only wavenumbers below some critical value, called Kolmogorov's dissipation number, are essential to describe the evolution of a thr…
On the determining wavenumber for the nonautonomous subcritical SQG equation
Alexey Cheskidov, Mimi Dai
A time-dependent determining wavenumber was introduced in [5] to estimate the number of determining modes for the surface quasi-geostrophic (SQG) equation. In this paper we continu…
Analysis of a diffuse interface model of multispecies tumor growth
Mimi Dai, Eduard Feireisl, Elisabetta Rocca +2
We consider a diffuse interface model for tumor growth recently proposed in [Y. Chen, S.M. Wise, V.B. Shenoy, J.S. Lowengrub, A stable scheme for a nonlinear, multiphase tumor grow…
Regularity criteria for the 3D Navier-Stokes and MHD equations
Alexey Cheskidov, Mimi Dai
We prove that a solution to the 3D Navier-Stokes or MHD equations does not blow up at provided $\displaystyle \limsup_{q \to \infty} \int_{\mathcal{T}_q}^T \|Δ_q(\nabla \time…