Continuability in time of smooth solutions of strong-nonlinear nondiagonal parabolic systems

Arina Arkhipova

Displaying similar documents to “Continuability in time of smooth solutions of strong-nonlinear nondiagonal parabolic systems”

Solvability problem for strong-nonlinear nondiagonal parabolic system

Arina A. Arkhipova (2002)

Mathematica Bohemica

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A class of $q$ -nonlinear parabolic systems with a nondiagonal principal matrix and strong nonlinearities in the gradient is considered.We discuss the global in time solvability results of the classical initial boundary value problems in the case of two spatial variables. The systems with nonlinearities $q \in (1, 2)$ , $q = 2$ , $q > 2$ , are analyzed.

Cauchy-Dirichlet problem in Morrey spaces for parabolic equations with discontinuous coefficients

Dian K. Palagachev, Maria A. Ragusa, Lubomira G. Softova (2003)

Bollettino dell'Unione Matematica Italiana

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Let $Q_{T}$ be a cylinder in $R^{n + 1}$ and $x = (x^{'}, t) \in R^{n} \times R$ . It is studied the Cauchy-Dirichlet problem for the uniformly parabolic operator $\{\begin{matrix} u_{t} - \overset{n}{\sum_{i, j = 1}} a^{i j} (x) D_{i j} u = f (x) & q.o. in Q_{T}, \\ u (x) = 0 & su \partial Q_{T}, \end{matrix}$ in the Morrey spaces $W_{p, λ}^{2, 1} (Q_{T})$ , $p \in (1, \infty)$ , $λ \in (0, n + 2)$ , supposing the coefficients to belong to the class of functions with vanishing mean oscillation. There are obtained a priori estimates in Morrey spaces and Hölder regularity for the solution and its spatial derivatives.

Extension of CR functions to «wedge type» domains

Andrea D&amp;#039;Agnolo, Piero D&#039;Ancona, Giuseppe Zampieri (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let $X$ be a complex manifold, $S$ a generic submanifold of $X^{R}$ , the real underlying manifold to $X$ . Let $Ω$ be an open subset of $S$ with $\partial Ω$ analytic, $Y$ a complexification of $S$ . We first recall the notion of $Ω$ -tuboid of $X$ and of $Y$ and then give a relation between; we then give the corresponding result in terms of microfunctions at the boundary. We relate the regularity at the boundary for ${\bar{\partial}}_{b}$ to the extendability of $C R$ functions on $Ω$ to $Ω$ -tuboids of $X$ . Next, if $X$ has complex dimension 2, we give results...

Regularity problem for one class of nonlinear parabolic systems with non-smooth in time principal matrices

Arina A. Arkhipova, Jana Stará (2019)

Commentationes Mathematicae Universitatis Carolinae

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Partial regularity of solutions to a class of second order nonlinear parabolic systems with non-smooth in time principal matrices is proved in the paper. The coefficients are assumed to be measurable and bounded in the time variable and VMO-smooth in the space variables uniformly with respect to time. To prove the result, we apply the so-called $A (t)$ -caloric approximation method. The method was applied by the authors earlier to study regularity of quasilinear systems.

The inviscid limit for density-dependent incompressible fluids

Raphaël Danchin (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

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This paper is devoted to the study of smooth flows of density-dependent fluids in $ℝ^{N}$ or in the torus $𝕋^{N}$ . We aim at extending several classical results for the standard Euler or Navier-Stokes equations, to this new framework. Existence and uniqueness is stated on a time interval independent of the viscosity $μ$ when $μ$ goes to $0$ . A blow-up criterion involving the norm of vorticity in $L^{1} (0, T; L^{\infty})$ is also proved. Besides, we show that if the density-dependent Euler equations have a smooth...