Well posedness of nonlinear parabolic systems beyond duality

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10401796" target="_blank" >RIV/00216208:11320/19:10401796 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=8kdkHGuV0L" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=8kdkHGuV0L</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.anihpc.2019.01.004" target="_blank" >10.1016/j.anihpc.2019.01.004</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Well posedness of nonlinear parabolic systems beyond duality

Popis výsledku v původním jazyce

We develop a methodology for proving well-posedness in optimal regularity spaces for a wide class of nonlinear parabolic initial-boundary value systems, where the standard monotone operator theory fails. A motivational example of a problem accessible to our technique is the following system partial derivative(t)u - div (nu(vertical bar del u vertical bar) = -div f with a given strictly positive bounded function v, such that lim(k -&gt;infinity)nu(k) = v(infinity) and f is an element of L-q with q is an element of (1, infinity). The existence, uniqueness and regularity results for q &gt;= 2 are by now standard. However, even if a priori estimates are available, the existence in case q is an element of (1, 2) was essentially missing. We overcome the related crucial difficulty, namely the lack of a standard duality pairing, by resorting to proper weighted spaces and consequently provide existence, uniqueness and optimal regularity in the entire range q is an element of (1, infinity). Furthermore, our paper includes several new results that may be of independent interest and serve as the starting point for further analysis of more complicated problems. They include a parabolic Lipschitz approximation method in weighted spaces with fine control of the time derivative and a theory for linear parabolic systems with right hand sides belonging to Muckenhoupt weighted L-q spaces. (C) 2019 Elsevier Masson SAS. All rights reserved.

Název v anglickém jazyce

Well posedness of nonlinear parabolic systems beyond duality

Popis výsledku anglicky

We develop a methodology for proving well-posedness in optimal regularity spaces for a wide class of nonlinear parabolic initial-boundary value systems, where the standard monotone operator theory fails. A motivational example of a problem accessible to our technique is the following system partial derivative(t)u - div (nu(vertical bar del u vertical bar) = -div f with a given strictly positive bounded function v, such that lim(k -&gt;infinity)nu(k) = v(infinity) and f is an element of L-q with q is an element of (1, infinity). The existence, uniqueness and regularity results for q &gt;= 2 are by now standard. However, even if a priori estimates are available, the existence in case q is an element of (1, 2) was essentially missing. We overcome the related crucial difficulty, namely the lack of a standard duality pairing, by resorting to proper weighted spaces and consequently provide existence, uniqueness and optimal regularity in the entire range q is an element of (1, infinity). Furthermore, our paper includes several new results that may be of independent interest and serve as the starting point for further analysis of more complicated problems. They include a parabolic Lipschitz approximation method in weighted spaces with fine control of the time derivative and a theory for linear parabolic systems with right hand sides belonging to Muckenhoupt weighted L-q spaces. (C) 2019 Elsevier Masson SAS. All rights reserved.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-12719S" target="_blank" >GA18-12719S: Thermodynamická a matematická analýza proudění strukturovaných tekutin</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Annales de l&apos;Institut Henri Poincaré C, Analyse Non Linéaire

ISSN

0294-1449

e-ISSN

—

Svazek periodika

36

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

FR - Francouzská republika

Počet stran výsledku

34

Strana od-do

1467-1500

Kód UT WoS článku

000482247300010

EID výsledku v databázi Scopus

2-s2.0-85062679610