Finite time blowup for parabolic systems in two dimensions
, 2016 We construct examples of finite time singularity from smooth data for linear uniformly parabolic systems in the plane. We obtain similar examples for quasilinear systems with coefficients that depend only on the solution.Comment: 16 ...
Mooney, Connor
core +1 more source
Blow-up of weak solutions to a chemotaxis system under influence of an external chemoattractant
, 2015 We study nonnnegative radially symmetric solutions of the parabolic-elliptic Keller-Segel whole space system \begin{align*} \left\{\begin{array}{c@{\,}l@{\quad}l@{\,}c} u_{t}&=\Delta u-\nabla\!\cdot(u\nabla v),\ &x\in\mathbb{R}^n,& t>0,\\ 0 &=\Delta v+u ...
Black, Tobias
core +1 more source
Green's functions for parabolic systems of second order in time-varying domains
, 2010 We construct Green's functions for divergence form, second order parabolic systems in non-smooth time-varying domains whose boundaries are locally represented as graph of functions that are Lipschitz continuous in the spatial variables and 1/2-H\"older ...
D. G. Aronson +31 more
core +1 more source
Higher integrability for doubly nonlinear parabolic systems
, 2018 This paper proves a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems. The new feature of the argument is that the intrinsic geometry involves the solution as well as its spatial gradient ...
Bögelein, Verena +3 more
core +1 more source
Partial regularity for parabolic systems with VMO-coefficients [PDF]
, 2013 We establish partial regularity for vector-valued solutions to parabolic systems where the coefficients are possibly discontinuous with respect to (x,t). More precisely, we assume a VMO-condition with respect to the (x,t) and continuity with respect to u
Kanazawa, Taku
core
Sturmian Multiple Zeros for Stokes and Navier--Stokes Equations in $\re^3$ via Solenoidal Hermite Polynomials [PDF]
, 2012 Multiple spatial zero formations for Stokes and Navier-Stokes equations in three dimensions are shown to occur according to nodal sets of solenoidal Hermite polynomials.
Galaktionov, V. A.
core
A Short Proof of Increased Parabolic Regularity
, 2015 We present a new, short proof of the increased regularity obtained by solutions to uniformly parabolic partial differential equations. Though this setting is fairly introductory, our new method of proof, which uses a priori estimates, can be extended to ...
Michalowski, Nicholas +1 more
core +1 more source
A diffusion problem with gradient constraint depending on the temperature [PDF]
, 2010 We consider a system of a variational inequality with gradient constraint depending on the temperature, coupled with the heat equation. We prove existence of solution of this system by approximating it by a system of equations and using a fixed point
Azevedo, Assis, Santos, Lisa
core
Higher integrability for doubly nonlinear parabolic systems. [PDF]
SN Partial Differ Equ Appl, 2022 Bögelein V, Duzaar F, Scheven C.
europepmc +1 more source
On Regularized Systems of Equations for Gas Mixture Dynamics with New Regularizing Velocities and Diffusion Fluxes. [PDF]
Entropy (Basel), 2023 Zlotnik A, Lomonosov T.
europepmc +1 more source