Remarks about Signorini's problem in linear elasticity
Remarks on regularity criteria for the Navier-Stokes equations with axisymmetric data
We consider the axisymmetric Navier-Stokes equations with non-zero swirl component. By invoking the Hardy-Sobolev interpolation inequality, Hardy inequality and the theory of (1 < β < ∞) weights, we establish regularity criteria involving , or in some weighted Lebesgue spaces. This improves many previous results.
Remarks on the a priori bound for the vorticity of the axisymmetric Navier-Stokes equations
We study the axisymmetric Navier-Stokes equations. In 2010, Loftus-Zhang used a refined test function and re-scaling scheme, and showed that By employing the dimension reduction technique by Lei-Navas-Zhang, and analyzing , and on different hollow cylinders, we are able to improve it and obtain
Remarks on the blow-up criterion for the MHD system involving horizontal components or their horizontal gradients
We study the Cauchy problem for the MHD system, and provide two regularity conditions involving horizontal components (or their gradients) in Besov spaces. This improves previous results.
Remarks on the Regularity of Weak Solutions to Some Variational Inequalities.
Remarks on the smoothness of the solutions of the 3-D Navier-Stokes equations.
Removable singularities for weak solutions of quasilinear elliptic systems.
Removeable singular sets of fully nonlinear elliptic equations.
Reverse smoothing effects, fine asymptotics, and Harnack inequalities for fast diffusion equations.
Riesz transform on manifolds and heat kernel regularity
Risultati di esistenza, regolarità e confronto per equazioni ellittiche
Risultati di regolarità, stabilità, instabilità e biforcazione per un problema a frontiera libera
Scaling limits and regularity results for a class of Ginzburg-Landau systems
Schauder theorems for linear elliptic and parabolic problems with unbounded coefficients in
We study existence, uniqueness, and smoothing properties of the solutions to a class of linear second order elliptic and parabolic differential equations with unbounded coefficients in . The main results are global Schauder estimates, which hold in spite of the unboundedness of the coefficients.
Second order parabolic systems, optimal regularity, and singular sets of solutions
Semielliptic singularities
Semilinear parabolic systems
Semilinear wave equations with angularly smooth data
Semilinear waves with cusp singularities
Serrin-type regularity criterion for the Navier-Stokes equations involving one velocity and one vorticity component
We consider the Cauchy problem for the three-dimensional Navier-Stokes equations, and provide an optimal regularity criterion in terms of and , which are the third components of the velocity and vorticity, respectively. This gives an affirmative answer to an open problem in the paper by P. Penel, M. Pokorný (2004).