Regularity results for parabolic systems related to a class of non-Newtonian fluids.
From MaRDI portal
Publication:1426663
DOI10.1016/j.anihpc.2002.11.002zbMath1052.76004OpenAlexW2011796284WikidataQ58880905 ScholiaQ58880905MaRDI QIDQ1426663
Giuseppe Mingione, Emilio Acerbi, Gregory A. Seregin
Publication date: 15 March 2004
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=AIHPC_2004__21_1_25_0
Smoothness and regularity of solutions to PDEs (35B65) Non-Newtonian fluids (76A05) PDEs in connection with fluid mechanics (35Q35) Magnetohydrodynamics and electrohydrodynamics (76W05) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)
Related Items
Pseudoparabolic equations with variable exponents and coefficients: blow-up and large time behaviors ⋮ Parabolic Harnack estimates for anisotropic slow diffusion ⋮ Temporal regularity of symmetric stochastic \(p\)-Stokes systems ⋮ On an application of Phragmén-Lindelöf method to singular fractional-order problem ⋮ Non-isothermal non-Newtonian fluids: The stationary case ⋮ Nonlocal hyperbolic Stokes system with variable exponent of nonlinearity ⋮ Hölder regularity for degenerate parabolic equations with variable exponents ⋮ The impact of intrinsic scaling on the rate of extinction for anisotropic non-Newtonian fast diffusion ⋮ A new variable exponent Picone identity and applictions ⋮ Existence and uniqueness of solution for a unilateral problem in Sobolev spaces with variable exponent ⋮ Diffusion convection equation with variable nonlinearities ⋮ On a p⋅-biharmonic problem of Kirchhoff type involving critical growth ⋮ Hölder continuity of weak solution to a nonlinear problem with non-standard growth conditions ⋮ Regularity for parabolic equations with time dependent growth ⋮ Blow-up properties in the parabolic problems with anisotropic nonstandard growth conditions ⋮ Existence of weak solutions of parabolic systems with \(p,q\)-growth ⋮ Existence of weak solutions for non-stationary flows of fluids with shear thinning dependent viscosities under slip boundary conditions in half space ⋮ Gradient estimates for Orlicz double phase problems with variable exponents ⋮ Existence,uniqueness, and nonexistence of solutions to nonlinear diffusion equations with \(p(x,t)\)-Laplacian operator ⋮ Long-time behavior of solutions to a class of parabolic equations with nonstandard growth condition ⋮ Existence and uniqueness of solutions of degenerate parabolic equations with variable exponents of nonlinearity ⋮ Renormalized and entropy solutions for nonlinear parabolic equations with variable exponents and \(L^{1}\) data ⋮ The boundary regularity of non-linear parabolic systems. II ⋮ The boundary regularity of non-linear parabolic systems I ⋮ Existence of solutions for the \(p(x)\)-Laplacian problem with singular term ⋮ Partial regularity for degenerate parabolic systems with nonstandard growth and discontinuous coefficients ⋮ Existence, uniqueness and blowup for hyperbolic equations with nonstandard growth conditions ⋮ Global higher regularity of solutions to singular \(p(x,t)\)-parabolic equations ⋮ Global a priori bounds for weak solutions to quasilinear parabolic equations with nonstandard growth ⋮ The stability of parabolic problems with nonstandard \(p(x,t)\)-growth ⋮ Evolutionary, symmetric \(p\)-Laplacian. Interior regularity of time derivatives and its consequences ⋮ Higher integrability of very weak solutions of systems of \(p(x)\)-Laplacean type ⋮ Geometric estimates for doubly nonlinear parabolic PDEs ⋮ Quasilinear parabolic problem with variable exponent: Qualitative analysis and stabilization ⋮ Very weak solutions of subquadratic parabolic systems with non-standard \(p(x, t)\)-growth ⋮ A new kind of the solutions of a convection-diffusion equation related to the \(p(x)\)-Laplacian ⋮ Generalized Kelvin-Voigt equations with \(p\)-Laplacian and source/absorption terms ⋮ Regularity for the weak solutions to certain parabolic systems under certain growth condition ⋮ Parabolic equations with \(p,q\)-growth ⋮ On the continuity of solutions of the nonhomogeneous evolution \(p(x, t)\)-Laplace equation ⋮ Parabolic systems with \({p,q}\)-growth: a variational approach ⋮ Weighted \(L^{q ( \cdot )}\)-estimates for the nonlinear parabolic equations with non-standard growth ⋮ Weighted Lorentz estimates for parabolic equations with non-standard growth on rough domains ⋮ A note on the existence and uniqueness of time-periodic electro-rheological flows ⋮ Sharp regularity estimates for quasilinear evolution equations ⋮ Existence and regularity results for a class of parabolic problems with double phase flux of variable growth ⋮ Hölder estimates for parabolic \(p(x, t)\)-Laplacian systems ⋮ Nonlinear diffusion equations driven by the \(p(\cdot)\)-Laplacian ⋮ Existence of solutions for the evolution \(p(x)\)-Laplacian equation not in divergence form ⋮ Removability of isolated singularity for anisotropic parabolic equations with absorption ⋮ Higher integrability for solutions to parabolic problems with irregular obstacles and nonstandard growth ⋮ Existence theorems for solutions of parabolic equations with variable order of nonlinearity ⋮ On the blow-up of solutions to anisotropic parabolic equations with variable nonlinearity ⋮ Existence of solutions to an initial Dirichlet problem of evolutional \(p(x)\)-Laplace equations ⋮ Long-time behavior for a nonlinear parabolic problem with variable exponents ⋮ Partial regularity for parabolic systems with non-standard growth ⋮ THE DIRICHLET PROBLEMS FOR NONLINEAR ELLIPTIC EQUATIONS WITH VARIABLE EXPONENTS ON RIEMANNIAN MANIFOLDS ⋮ Strong solutions of evolution equations with \(p(x,t)\)-Laplacian: existence, global higher integrability of the gradients and second-order regularity ⋮ Non-Newtonian fluids with discontinuous-in-time stress tensor ⋮ Existence of solutions for the \(p(x)\)-Laplacian problem with the critical Sobolev-Hardy exponent ⋮ Regularity of weak solutions to a class of nonlinear problem with non-standard growth conditions ⋮ Existence of local strong solutions for motions of electrorheological fluids in three dimensions ⋮ Quasilinear parabolic problem with \(p(x)\)-Laplacian: existence, uniqueness of weak solutions and stabilization ⋮ The one dimensional parabolic \(p(x)\)-Laplace equation ⋮ Compact embedding for \(p(x,t)\)-Sobolev spaces and existence theory to parabolic equations with \(p(x,t)\)-growth ⋮ Regularity of minima: an invitation to the dark side of the calculus of variations. ⋮ Hölder continuity of solutions of parabolic equations with variable nonlinearity exponent ⋮ The Cauchy-Dirichlet problem for a general class of parabolic equations ⋮ Nonlocal variational principles with variable growth ⋮ Extinction in finite time of solutions to the nonlinear diffusion equations involving \(p(x,t)\)-Laplacian operator ⋮ Variable exponent spaces of differential forms on Riemannian manifold ⋮ Partial regularity and singular set of solutions to second order parabolic systems ⋮ Some properties of solutions for an evolution \(p(x)\)-Laplacian equation ⋮ Study of the solutions to a model porous medium equation with variable exponent of nonlinearity ⋮ Calderón-Zygmund estimates for parabolic \(p(x,t)\)-Laplacian systems ⋮ The Neumann boundary value problem of higher order quasilinear elliptic equation ⋮ Overview of differential equations with non-standard growth ⋮ The blow-up of solutions for \(m\)-Laplacian equations with variable sources under positive initial energy ⋮ Existence of weak solutions of doubly nonlinear parabolic equations ⋮ A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions ⋮ Partial regularity of a certain class of non-Newtonian fluids ⋮ Weak Harnack estimates for quasiminimizers with non-standard growth and general structure ⋮ Blow-up of solutions to parabolic equations with nonstandard growth conditions ⋮ Self-improving property of nonlinear higher order parabolic systems near the boundary ⋮ Anisotropic parabolic equations with variable nonlinearity ⋮ Elliptic equations and systems with nonstandard growth conditions: existence, uniqueness and localization properties of solutions ⋮ Lipschitz regularity for viscosity solutions to parabolic \({p(x,t)}\)-Laplacian equations on Riemannian manifolds ⋮ Partial regularity and singular sets of solutions of higher order parabolic systems ⋮ Harmonic type approximation lemmas ⋮ Behavior of solutions of the Dirichlet Problem for the $p(x)$-Laplacian at a boundary point ⋮ A remark on finite element approximation of singular parabolic p(x, t)-Laplacian equation ⋮ Electro-rheological fluids under random influences: martingale and strong solutions ⋮ Doubly nonlinear equation involving \(p(x)\)-homogeneous operators: local existence, uniqueness and global behaviour ⋮ Global estimates for solutions of singular parabolic and elliptic equations with variable nonlinearity ⋮ Interior and boundary higher integrability of very weak solutions for quasilinear parabolic equations with variable exponents ⋮ On the sufficient condition for regularity of a boundary point for singular parabolic equations with non-standard growth ⋮ Geometric \(C^{1 + \alpha}\) regularity estimates for nonlinear evolution models ⋮ The principle of concentration compactness in \(L^{p(x)}\) spaces and its application ⋮ Extinction of solutions of parabolic equations with variable anisotropic nonlinearities ⋮ Inverse problem for an equation with a nonstandard growth condition ⋮ The boundedness and Hölder continuity of weak solutions to elliptic equations involving variable exponents and critical growth ⋮ Existence of weak and renormalized solutions of degenerated elliptic equation ⋮ Unnamed Item ⋮ Parabolic Systems with Polynomial Growth and Regularity ⋮ The Dirichlet problem of higher order quasilinear elliptic equation ⋮ Classification of blow-up and global existence of solutions to an initial Neumann problem ⋮ A strong maximum principle for differential equations with nonstandard \(p(x)\)-growth conditions ⋮ Existence and uniqueness of bounded weak solutions for some nonlinear parabolic problems ⋮ Second order parabolic systems, optimal regularity, and singular sets of solutions ⋮ Local continuity of singular anisotropic parabolic equations with variable growth
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the nonlinear parabolic systems in divergence form. Hölder continuity and partial Hölder continuity of the solutions
- Growth conditions and regularity. A counterexample
- Flow of electro-rheological materials
- Full regularity for a class of degenerated parabolic systems in two spatial variables
- Variants of the Stokes problem: the case of anisotropic potentials
- The singular set of solutions to non-differentiable elliptic systems
- Variational methods for problems from plasticity theory and for generalized Newtonian fluids
- Regularity results for electrorheological fluids: The stationary case
- Navier-Stokes equations with lower bounds on the pressure
- Regularity results for stationary electro-rheological fluids
- Sharp regularity for functionals with (\(p\),\(q\)) growth
- Interior regularity for solutions to the modified Navier-Stokes equations
- On partial regularity of suitable weak solutions to the three-dimensional Navier-Stokes equations
- Regularity and existence of solutions of elliptic equations with p,q- growth conditions
- Hölder continuity of the gradient of p(x)-harmonic mappings
- Variational methods for fluids of Prandtl-Eyring type and plastic materials with logarithmic hardening
- Flow of shear dependent electrorheological fluids
- Partial regularity of suitable weak solutions of the navier-stokes equations
- On the number of singular points of weak solutions to the Navier-Stokes equations
- Regularity results for a class of functionals with non-standard growth
- Mathematical modeling of electrorheological materials
- On weak solutions to a class of non-Newtonian incompressible fluids in bounded three-dimensional domains: The case \(p\geq 2\)
- Partial regularity for variational integrals with \((s,\mu,q)\)-growth