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03569aam a2200469 i 4500 001 0F8BB0FA177D11EC850ADFAD22ECA4DB 003 SILO 005 20210917010313 008 210507t20212021riu b 000 0 eng 010 $a 2021016988 020 $a 1470444216 020 $a 9781470444211 035 $a (OCoLC)1228928456 040 $a LBSOR/DLC $b eng $e rda $c DLC $d OCLCO $d OCLCF $d MNU $d OCLCO $d PAU $d NUI $d SILO 042 $a pcc 100 1 $a Godin, Paul, $e author. 245 14 $a The 2D compressible Euler equations in bounded impermeable domains with corners / $c Paul Godin. 246 3 $a Two-dimensional compressible Euler equations in bounded impermeable domains with corners 264 1 $a Providence, RI : $b American Mathematical Society, $c [2021] 300 $a v, 72 pages ; $c 26 cm. 490 1 $a Memoirs of the American Mathematical Society, $x 0065-9266 ; $v number 1313 500 $a "January 2021, volume 269, number 1313 (fourth of 7 numbers)." 504 $a Includes bibliographical references (pages 71-72). 505 0 $a Statement of the results -- The associated linear Euler equations (C[infinity] coefficients) -- Proof of proposition 3.3 and of proposition 3.4, and more estimates -- The associated linear Euler equations (non-C[infinity] coefficients) -- Proof of theorem 2.1, theorem 2.2, remark 2.1, remark 2.2. 520 $a "We study 2D compressible Euler flows in bounded impermeable domains whose boundary is smooth except for corners. We assume that the angles of the corners are small enough. Then we obtain local (in time) existence of solutions which keep the L2 Sobolev regularity of their Cauchy data, provided the external forces are sufficiently regular and suitable compatibility conditions are satisfied. Such a result is well known when there is no corner. Our proof relies on the study of associated linear problems. We also show that our results are rather sharp: we construct counterexamples in which the smallness condition on the angles is not fulfilled and which display a loss of L2 Sobolev regularity with respect to the Cauchy data and the external forces"--Provided by publisher. 650 0 $a Lagrange equations $x Numerical solutions. 650 0 $a Boundary value problems $x Numerical solutions. 650 0 $a Differential equations, Hyperbolic. 650 0 $a Gas dynamics $x Mathematics. 650 7 $a Boundary value problems $x Numerical solutions. $2 fast $0 (OCoLC)fst00837129 650 7 $a Differential equations, Hyperbolic. $2 fast $0 (OCoLC)fst00893463 650 7 $a Gas dynamics $x Mathematics. $2 fast $0 (OCoLC)fst00938244 650 7 $a Lagrange equations $x Numerical solutions. $2 fast $0 (OCoLC)fst00990774 650 7 $a Partial differential equations -- Partial differential equations of mathematical physics and other areas of application -- Euler equations. $2 msc 650 7 $a Fluid mechanics -- Compressible fluids and gas dynamics, general -- Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics. $2 msc 650 7 $a Partial differential equations -- Hyperbolic equations and systems -- Initial-boundary value problems for first-order hyperbolic equations. $2 msc 650 7 $a Partial differential equations -- Hyperbolic equations and systems -- Nonlinear first-order hyperbolic equations. $2 msc 773 18 $w 990007620060202771 $g no:31858071391712 830 0 $a Memoirs of the American Mathematical Society ; $v no. 1313, $x 0065-9266 941 $a 1 952 $l OVUX522 $d 20220317030003.0 956 $a http://locator.silo.lib.ia.us/search.cgi?index_0=id&term_0=0F8BB0FA177D11EC850ADFAD22ECA4DBInitiate Another SILO Locator Search